The team announced Sunday that Ramirez was placed on the 10-day injured list. Indians manager Terry Francona told reporters that hand specialist Dr. Thomas Graham will perform the procedure Monday in New York.
The Indians didn't provide a timetable for his return, but the injury typically requires over a month to heal.
"Dr. Graham will then lay out what he thinks timetables, potential timetables," Francona said. "I'm not sure anybody's ever going to be able to nail it exactly. But we will have a much better idea after he does the procedure.
"I feel bad for Josey. There's two ways to look at it: You can feel sorry for yourself, which probably doesn't end well, or you can choose to fight back and feel like this is our time to shine. And I would choose No. 2. I'm aware that it got more difficult. We lost a great player. That doesn't mean you can't win. Just makes it a little harder."
Ramirez, a two-time All-Star, underwent an MRI after he exited in the first inning of Saturday's contest against the Kansas City Royals. He doubled over in pain and grabbed his wrist after fouling off a pitch from Royals starter Glenn Sparkman.
Ramirez, 26, has a .254 batting average with 20 home runs and 75 RBIs in 126 games this season.
Mike Freeman replaced Ramirez in the lineup during Saturday's game against the Royals. The Indians also called up infielder Yu Chang from Triple-A Columbus in a corresponding roster move.