The operation was performed at Georgetown University Hospital.
O'Connor, 58, was appointed to the court by President Reagan in 1981 as the first and only woman Supreme Court justice in the nation's history.
She issued a brief statement that said, "The prognosis is for total recovery. I do not anticipate missing any oral arguments."
The court is in a two-week recess, due to return to the bench on Oct. 31.
"I underwent surgery for breast cancer. It was found to exist in a very early form and stage," O'Connor's statement said.
The statement did not say whether the surgery was for removal of a lump or the entire breast. There also were no further details on whether the justice will receive any form of continuing treatment.
A cancer expert, Dr. Robert S. Siegel, said her intention to return to work in just 10 days would mean "a remarkably fast recovery" and may be good news for her prognosis.
Siegel, who is assistant professor of medicine and director of a cancer treatment unit at George Washington University Hospital, said that would be "a pretty quick return to work."
Siegel was not involved in O'Connor's case, and he was commenting generally on conditions such as hers. But he said the speed with which she plans to return to work may indicate the cancer was caught at a very early time and that there is no indication it has spread to other organs in the body.
Siegel said lumpectomy patients usually are released from the hospital in three days to four days, but usually return in two weeks to start radiation therapy. Patients who have a breat removed do not require the radiation therapy and usually return to work within two weeks to three weeks, he said.
O'Connor's health, as far as is publicly known, has been good. She underwent an appendectomy in March and she was soon back at work.
Supreme Court justices generally are sparing, at best, in disclosing details of their health.
O'Connor's appointment to be a justice seven years ago ended 191 years of male exclusivity on the high court.
A political and judicial conservative, she has been a champion of states' rights and enhanced police power.
But while she generally sides with the conservative wing of the court anchored by Chief Justice William H. Rehnquist, she has cast important moderate votes in such areas as sex discrimination and affirmative action.
She was a virtual unknown on the national scene when Reagan picked her to replace Potter Stewart, who had retired.
O'Connor served as an Arizona state judge and before that was a member of that state's Legislature.