Upton, who had doubled and struck out in his previous two trips to the plate, swung at a 1-1 pitch from O's left-hander Brian Burres, then crumpled to the ground holding his left shoulder.
Upton suffered the same type of injury on Aug. 17, 2006, and missed three games.
"The guys from Tampa Bay have seen it happen before, so it's nothing new," Upton said. "It looks bad right away. It feels bad right away. But this is the best it's ever felt right after, so we shouldn't think too much of it."
While Upton said he's not sure exactly when he'll be back, Rays manager Joe Maddon said he expects Upton to be available on Friday night against the Red Sox.
"He's doubtful as a starter, but he'll probably be ready to help us out at some point during the game," Maddon said. "And then we'll evaluate going into Saturday. But I don't think it's long-term. Similar to what happened [in '06], but not as severe."
Nathan Haynes replaced Upton and finished Upton's at-bat by striking out; according to scoring rules, the strikeout went down as Upton's.
Upton is hitting .294 with three home runs and 21 RBIs.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.