Morse underwent an MRI exam on Tuesday, which confirmed the nature of his injury.
Morse, 32, has appeared in 130 games, 16 shy of the career high he reached with Washington in 2011. He has started 125 games, including 82 in left field, 39 at first base and four as a designated hitter.
The right-handed hitter is batting .280 with 16 home runs, 61 RBIs and a .477 slugging percentage.
Chris Haft is a reporter for MLB.com. Read his blog, Haft-Baked Ideas, and follow him on Twitter at @sfgiantsbeat. This story was not subject to the approval of Major League Baseball or its clubs.