That's much longer than the two weeks it was initially thought Sheets would be out of action. It was decided after an ultrasound Tuesday.
The NL All-Star was injured Saturday in his outing against Colorado and was placed on the 15-day disabled list.
He is disheartened, with the Brewers fighting for a possible National League Central title this season.
"I want to be a part of it," the 28-year-old Sheets said on the Brewers' Web site. "We're in the middle of a pretty intense time right now, and I don't want to be on the sidelines."
"We just have to be on top of things in case there's another injury," said Manager Bob Melvin.
Sheets is 10-4 with an ERA of 3.39 this season, with 90 strikeouts and just 25 walks in 119 1/3 innings.
Notable deaths of 2014 [PHOTOS]