The Sisters of Providence, an order of Catholic nuns, has decided to close two schools they operate at Tenley Circle NW and sell the property to provide funds for the retirement and medical care of its aging members.

The 8.2 acre campus, occupied by Immaculata Preparatory School, a high school for girls, and Immaculata Dunblane, a grammar school and junior high, will be sold for $7.6 million to American University, according to announcements by the Catholic order and the university.

American University officials indicated that the purchase will be financed through long-term borrowing and fund raising "that will not have an adverse impact on the university's operating budget."

Settlement and transfer of the property, at Wisconsin and Nebraska avenues NW, will take place shortly after the two schools close in June 1986, the announcements said.

The schools, which were established at the site in 1905, now enroll about 600 students, all girls. A statement issued by the headquarters of the order in St. Mary-of-the-Woods, Ind., said the sale was "forced . . . by overriding economic circumstances," caused by a decline in new members since the mid-1960s, "coupled with the rapid increase in the number of infirm and retired sisters."

Of the order's national membership of 955, the statement said, more than a third are over 70 years old, and only about half the nunsare able to work full time, which "is inadequate to support such a large community."

About 90 of the elderly nuns need skilled or assisted nursing care, the statement said, while 70 others receive regular medical treatment.

"This is a very sad day for us," said Sister Anne Doherty, general superior of the order. "There is no relief for the pain our sisters, our excellent lay faculty, staff, and students feel at the loss . . . . We are grateful that the work of education will continue at this site."

American University President Richard Berendzen said purchase of the property is "a wonderful thing for us." Berendzen said it would relieve "inadequate facilities" on the university's main campus at Massachusetts and Nebraska avenues NW, just under a mile from the Immaculata site.

Although the exact use of the property and its four buildings has not been determined, he said parts of it may house classes in the performing arts or continuing education.

In 1978, Immaculata College, a two-year women's college that occupied part of the property, was closed. Since then, its dormitory and some of its classrooms have been leased to American University.

The college was closed because of declining enrollment and rising costs, but enrollment at the other two schools remains high with more than two students applying for each one accepted, according to a profile of the school published last year. Last year the high school had about 480 students in grades 9 through 12, while the lower school had about 135. Tuition at the high school is $2,300 a year.

The statement said that 10th-grade students at the school will be able to take a special accelerated course, allowing them to graduate with the current junior class in the spring of 1986. Current 7th- and 8th-graders will be allowed to complete their studies. All other students will have to enroll in other schools next fall, according to the statement.

The Sisters of Providence, which owns and operates the school, is a self-supporting order separate from the Archdiocese of Washington, which runs the area's Catholic parochial schools. In recent years, the order's statement said, it has sold schools in Indiana, Illinois and California to provide money for the Sisters of Providence Retirement Fund.

It said all the money from the Washington sale also will be placed in the retirement fund, which now spends about $3 million a year.