Dr. Doug Carlen, the team's specialist, will perform the surgery.
"Everybody feels it's in his best interests for a quicker heal time," manager Kevin Cash said. "It sounds fairly standard. You have the surgery, go in for four- or five-week checkups, revisit it. We're rough estimating it at 8-10 weeks.
"The reality is, 8-10 weeks is a really long time to be out. But we'll find a way to get through it. That's a long time to go without a player as good as he is."
Mikie Mahtook, called up to fill the roster spot, was in the starting lineup on Monday in the first of two games at Marlins Park. The 26-year-old 2011 first-round pick out of LSU hit .356 last September, belting five homers in his final 23 at-bats.
He set a Rays rookie record with five hits on Sept. 18 against the Orioles.
"I think what Mikie did for us in a month last season was pretty special," Cash said. "Hopefully, he comes up here with that same type of confidence and the same energy that he provided for us at the end of the year. It was pretty considerable.
"We need that right now with K.K. out, Logan Forsythe out; we're missing two big parts to our offense."
Cash said he would employ a combination of players in center field.
"Desmond [Jennings]. Mikie, Brandon [Guyer], they'll all get some time in center, especially given the schedule that we have right now," Cash said. "We'll have to rotate them all through."
The Rays' next off-day is June 9.
Right-hander Brad Boxberger (adductor surgery) made his fourth official rehab appearance Sunday for Triple-A Durham, striking out two in an inning of work. His next appearance has yet to be determined.
Glenn Sattell is a contributor to MLB.com based in Miami.