Flaherty sustained the injury running the bases on the final play in a 4-2 loss to Toronto on Wednesday night.
Flaherty joins shortstop J.J. Hardy and second baseman Jonathan Schoop on the Orioles' DL.
The Orioles recalled infielder Rey Navarro from Triple-A Norfolk to help fill the void. The 25-year-old Navarro has not yet been in a major league game. He has played in 885 minor league games over nine minor league seasons.
Flaherty was batting .300 with two homers and four RBIs in nine games this season.