The Astros said Gattis, 29, will report to spring training on time and rehab with the team's medical staff. A designated hitter, he is coming off his best offensive season, with 27 home runs and 88 RBIs in his first year with the Astros after spending his first two major league seasons with the Atlanta Braves.
Gattis has an arbitration hearing scheduled for next Tuesday, with the Astros offering $3 million and Gattis asking for $3.8 million.
If his recovery goes as expected, Gattis would be back in time to get into some spring training games before Houston opens the 2016 season April 4 against the New York Yankees at Yankee Stadium.
The Houston Chronicle first reported the surgery, with MLB.com learning that the surgery took place Tuesday.