Supreme Court Justice Harry A. Blackmun is undergoing treatment for prostatic cancer at the Mayo Clinic in Rochester, Minn., a hospital spokeswoman said yesterday.

Blackmun, 78, is receiving out-patient treatment of an undisclosed nature "which is not incapacitating and is short-term," according to spokeswoman Meg Black. "The prognosis is excellent."

Doctors found "a small and localized recurrence of prostatic carcinoma" when Blackmun went to the hospital this month for a routine physical examination, she said.

Blackmun underwent surgery in 1977 for removal of his prostate after it was determined to be cancerous. The recurrence was found "in tissue nearby," Black said. She declined to say how long the treatment, which in similar cases is radiation therapy, would take.

Blackmun underwent surgery July 1 for hernia repair, the hospital said yesterday. Blackmun's chambers on Friday said he was vacationing in Wisconsin and swimming and taking walks. There was no mention of the cancer treatment, which apparently began over the weekend.

Blackmun had canceled a scheduled appearance last week at a judicial conference in Colorado Springs, Colo. Judges at the conference said they understood that Blackmun did not speak because of a scheduling conflict.

Prostate cancer is the third most common cancer in men, after skin cancer and lung cancer, according to the American Cancer Society. Medical experts said yesterday that it was most likely that the new growth was of a slow-growing type and probably detected at an early stage, since Blackmun receives frequent examinations.

Blackmun, the court's third-oldest justice, was appointed by President Richard M. Nixon in 1970. He began as a solid member of the conservative wing, siding frequently with his longtime friend, former chief justice Warren E. Burger.

By the mid-1970s, however, Blackmun began voting increasingly with the liberal wing of the court and is now seen as a strong member of the moderate-liberal group, especially on noncriminal matters.

Blackmun wrote the court's opinion in 1973 in Roe v. Wade, establishing a constitutional right to abortion.