Jean Struven Harris, headmistress of the exclusive Madeira School near McLean, was charged yesterday with murdering Dr. Herman Tarnower, creator of the popular "Scarsdale Diet," in an upstairs bedroom of his $500,000 home in fashionable Westchester County, N.Y.

Tarnower, 69, who credited Harris in his best-selling book with "splendid assistance in the research and writing," was found unconscious late Monday night in his pajamas, lying between two twin beds and bleeding profusely from three bullet wounds in his head, arm and chest. He died shortly before midnight on Monday at a hospital in White Plains, N.Y.

Harris, 56, a slim blond woman who has been headmistress for three years at the school, which trains the daughters of some of Washington's most affluent and powerful residents, was arraigned yesterday in Harrison, N.Y. She was ordered held in the Westchester County jail on a charge of second-degree murder.

Harrison Police Chief William P. Harris said the woman was charged after "she admitted that she had shot" Tarnower.

The shooting was reported by Tarnower's housekeeper, Suzanne van der Vreken, who told police she had heard sounds of a struggle and gunshots and feared a burglar was in the house.

The police chief said Harris, who had known Tarnower for 14 years and who was a frequent visitor to his posh red brick and glass home in Harrison, was seen driving away from Tarnower's house just as police arrived. h

Harris, according to police, turned her car around, went back up the 500-foot driveway to Tarnower's home and told an investigating officer, "There's been a shooting."

Police said she then turned over a .32-caliber Smith and Wesson revolver, which she took from the glove compartment of her blue and white 1973 Chrysler sedan. Police said they believe the revolver is the weapon used in the slaying.

Joel Arnow, Harris' lawyer, said yesterday that the headmistress arrived at Tarnower's house shortly before the 11 p.m. shooting and an argument broke out.

"Nothing I have learned so far would support a charge of intentional homicide," said Arnow, who interviewed his client yesterday for a little more than an hour. While he refused to explain the reasons for the argument, Arnow did say it was not over Tarnower's phenomenally successful diet book, which has sold nearly 3 million copies in hardback and paperback.

The lawyer would say only "no comment" to questions about a romantic relationship between Harris, who has been divorced for 14 years, and Tarnower, who has never been married.

Harris appeared in court yesterday with a bruise on the right side of her upper lip. Her lawyer said she suffered the bruise after entering Tarnower's home, which overlooks a pond with a tiny island and a stone statue of a Buddha.

Students and parents at Madeira School, where tuition for boarding students is $6,100 a year and $3,800 a year for day students, yesterday expressed shock at news of the murder and staunchly defended their headmistress.

"Mrs. Harris is a fine woman and a fine headmistress and no matter what happens I will always believe in her," said Laura Gill, 17, president of the day-school students.

Parents contacted yesterday said that Harris, who came to Madeira after serving as director of three other private schools in the East and Midwest and as a sales manager for Allied Maintenance Corp. in New York, was an "enlightened individual" and "the finest headmistress in the history of Madeira."

Harris received a standing ovation from mothers attending a school meeting last October when she said many of the students at Madeira needed strict discipline. Harris announced she had made the Georgetown area of Washington off-limits to students from the school.

Some students and parents, who asked to be unidentified, said yesterday that Harris was under some stress stemming from a disciplinary incident last Friday at the school.

Harris expelled four students after marijuana and smoking paraphernalia were found in dormitory rooms. The headmistress, who addressed the school's 325 students on public affairs each week, announced the expulsion at a meeting where several students voiced their disagreement with the dorm search and the expulsion procedures used by the administration.

One member of the school's board of directors said Harris showed no signs of stress last Friday night. She said Harris was planning to stay on the school's campus, where she lives alone in a single-story red brick house, for the three-week spring vacation, which began on Monday.

In Westchester County, Harris' lawyer said that the headmistress had "not been unexpected" when she arrived at Tarnower's home shortly before the shooting. The house is located along Purchase Street in Harrison, a street lined with mansions owned by prominent New York businessmen such as publisher Alfred A. Knopf.

Arnow, the laywer, said yesterday that the headmistress tried to call police after the shooting. The lawyer said she found the telephone out of order and was driving off in search of another phone when she saw the police approaching Tarnower's home.

Arnow said that the phone still wasn't working when police tried it later.

In court yesterday, Harris appeared exhausted and frequently rested her chin in her clasped hands. She wore a mink jacket, tan slacks and a green blouse brought to her by a friend. Police confiscated the clothes she was wearing when she was inside Tarnower's house.

Tarnower, who told friends that he had never married because he was wedded to his work, was a well-known cardiologist and internist who practiced medicine in the affluent community of Scarsdale, from which his book draws its name.

Tarnower found and was the senior member of the Scarsdale Medical Center, where he was to have been honored next month at a special dinner. "The Complete Scarsdale Medical Diet" was the second best-selling hardback book of 1979.

Samm Sinclair Baker, coauthor of the volume, described Tarnower yesterday as a "very sedate, private and austere man" who rarely spoke of his personal life. Baker said he once had attended a dinner party at Tarnower's home when Harris was a guest, but that he didn't know the extent of their relationship.

Tarnower "is the type of man you'd think was the chairman of General Motors. He is warm but remote," said Baker.

Tarnower frequently traveled on hunting and golfing trips when he wasn't working, Baker said. Baker said he believed Tarnower didn't have time for marriage.

At the Madeira School, a 74-year-old, 400-acre preparatory school for girls overlooking the Potomac River, administration officials held a press conference yesterday amid tight security and announced that Harris intends to resign as headmistress.

"We are not disturbed by the unfortunate events that affect Mrs. Harris," said Alice W. Faulkner, the school president. "We hope (the slaying) will have no effect on the school. We feel we have a very fine, very strong, very healthy school."

In 1973, the school was stunned when the partially clad body of a 14-year-old student from Arlington was found bound to a tree on the campus. The death of the student, who was the victim of a sex-related murder, troubled students and faculty at the school for several years.

Harris, who came to Maderia to replace headmistress Barbara Keyser, brought with her 20 years of teaching experience in everything from nursery school to directing a preparatory school.

According to students at Madeira, Harris frequently speaks to the assembled students about the need for "integrity" in one's personal and business life.

"She has said that word 'integrity' so many times that some of the students called her "Integrity Harris," said Sonya Knight, a senior and student president of the boarding school students.

Harris, according to Knight, stiffened the school's honor code and lectured the students frequently about their responsibility not to cheat or violate school rules involving the use of drugs.

Yet, Knight said, Harris was not considered an inflexible disciplinarian. At assembly each Monday morning she spoke about current events and public repsonsbility and led them, with her loud, clear voice, in singing hymns.

Harris was popular among many students, according to several interviewed yesterday. Last fall when her dog ran away, students gave her a new one named Cider as a Halloween gift.

An educational consulting firm last year gave Harris high marks as an administrator, calling her work "properly organized, responsible and effective . . . We are impressed with what the headmistress has accomplished in her two years at the school . . ."

Harris was born in Cleveland and raised in Shaker Heights, Ohio. One of her sons is in the Marine Corps and the other is in college.

The headmistress, who is scheduled to appear in Harrison Thursday for a preliminary hearing, was described yesterday by her lawyer as "in shock." The police chief in Harrison said Harris "is one of the nicest ladies we've ever had" in the jail.