Judge Shirley M. Hufstedler received a commitment that she will "not be precluded" from appointment to the Supreme Court before accepting President Carter's offer to head the new Education Department, White House officials said yesterday.

The nomination of Hufstedler, a judge on the 9th U.S. Circuit Court of Appeals and the highest ranking woman jurist in the United States, to be the nation's first secretary of education was formally made yesterday.

In a prepared statement, the president said Hufstedler "has one of the best minds in the country," and stressed his desire that the first education secretary bring fresh ideas to the job of directing the federal effort.

"I wanted a strong, creative thinker who could take a new, fresh look at the way we educate our children," Carter said in the statement. "In Judge Shirley Hufstedler, we have found that person."

White House deputy press secretary Rex Granum, who announced the appointment, said the subject of a possible future appointment to the Supreme Court came up Monday during a conversation between the president and Hufstedler.

He said there was no understanding reached during the meeting, but that Hufstedler was assured that she would not be precluded from consideration for future Supreme Court vacancies.

Granum declined to say who raised the subject of a future judicial appointment. However, Vice President Mondale later told reporters that it was Hufstedler. He quoted her as saying that while she was eager to accept the Education Department job she did not want to be disqualified for consideration for a Supreme Court seat.

Mondale said he did not consider this a condition for accepting the Cabinet job.

Hufstedler, 54, who lives in Pasadena, Calif., has frequently been mentioned as a potential Supreme Court nominee. She would likely figure in speculation over the next court vacancy, which could occur next summer. Justice William J. Brennan Jr. is reportedly considering retiring at the end of the court's current term and planning to make a decision on retirment in December.

Hufstedler did not appear at the White House for yesterday's announcement, but issued a written statement saying she expects "to spend a great deal of time as secretary of education listening to parents, teaches, students and other people who care about education in this nation. The first concern of this country in education must be helping all students to learn."

In choosing Hufstedler for the Education Department position, the president stepped outside the often rival segments in the education establishment to make a somewhat surprising appointment. Granum said this was deliberate and was based on Carter's desire "to have someone who could take a fresh, innovative look" at the way American education is run.

Hufstedler practiced law for 10 years in Los Angeles until 1961, when she was appointed to the Los Angeles County Superior Court. She later served on the state appellate court before her appointment in 1969 to the 9th U.S. Circuit Court of Appeals.

While she has associations with higher education -- she is chairman of the University of California Law Center Board of Trustees and a member of the Occidental College and California Institute of Technology Boards of Trustees -- she has no professional experience in the education field.