Rivera, 42, said that the procedure was scheduled after he learned that the blood clot discovered in his right calf after the May 3 injury was no longer an issue.
"I'll do what I have to do," Rivera said. "It's something I have to work at."
Dr. David Altchek, the Mets' medical director, will perform Rivera's procedure at the Hospital for Special Surgery in New York. Rivera has been working out since his injury, strengthening the knee to prepare it for surgery.
"Actually, I've been so busy with therapy that I don't even think about it," Rivera said. "When I come home, I'm tired, and then watching the games -- it's a full day."
Rivera vowed one day after the injury that he would return to a big league mound next season. Though he said that he does not want to consider any timetables for a complete recovery, Rivera confirmed that his intent to pitch again has not wavered.
"There's no doubt about that, God willing," Rivera said. "I always believe in miracles, a lot of good things. We've got to get it fixed first."
Rivera stamped out speculation about pitching again in 2012, saying, "I can't. I don't want to think about it. I guess miracles happen, but I just have to be able to do what I will do."
In Rivera's absence, the Yankees briefly promoted David Robertson to the closer's role before also losing him to injury. Rafael Soriano entered Wednesday's game a perfect 8-for-8 in save opportunities and appears to have secured the job, even as Robertson is expected to return from the disabled list in about a week.