The injury doesn't appear to be overly serious, and while Encarnacion likely will sit out the series finale on Thursday, he also wouldn't completely rule out the possibility of playing.
"I don't think it's anything bad," Encarnacion said following Wednesday's game. "I'll see tomorrow if I need maybe one day or maybe I feel I can play DH. We'll see tomorrow."
Designated hitter Adam Lind likely will see the bulk of the playing time at first base if Encarnacion requires some additional rest. Juan Francisco also could see action at designated hitter, which would then allow Brett Lawrie to move back to third base for a brief stint.
Encarnacion is coming off arguably the best month of his career. The 31-year-old tied Mickey Mantle for the most home runs by an American League player with 16 homers in May. He also posted a .281 average with a 1.132 OPS, 33 RBIs and 16 walks over the span of 30 games.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.