While appearing at a Salvation Army event at the Marriott Marquis hotel in New York, baseball's all-time saves leader said he will be unable to speak for a week following the surgery at New York-Presbyterian Hospital.
A raspy-voiced Rivera said he should begin to recover a week after the procedure.
"I don't like surgeries, but the sooner, the better," Rivera said. "I was worried about what caused it and what kind it is -- is it benign? I don't know. I'm [thinking] positive. We have to send it to the lab, and hopefully it's a good thing."
Rivera said last week that the condition has been bothering him for a month and that it has grown worse each time he speaks.
Given the relatively short recovery time, it's unlikely that the procedure will have any major effect on Rivera heading into next season.
"I talked to the doctor and she said it doesn't look ... serious," Rivera said. "But again, you have to take it to the lab and we'll find out."
Rivera, who turned 42 on Tuesday, enjoyed another excellent season in 2011, eclipsing Trevor Hoffman to set the Major League record for career saves.
The closer had 44 saves, bringing his career total to 603, while posting a 1.91 ERA -- his fourth straight season with an ERA below 2.00 and a WHIP under 1.00.
Rivera was presented with the Salvation Army's Pinnacle of Achievement Award, singling out individuals who have made differences to others in their personal and professional lives.
"Mo is so much more than the greatest closer in the history of Major League Baseball," said Lt. Col. Guy D. Klemanski, the Salvation Army's divisional commander for New York. "He is a caring and genuine individual who believes in making a difference for others."