The Rays made the roster move Monday, one day after Morton exited his start against the New York Yankees in the third inning.
Morton said he initially felt some tightness in his right shoulder during the second inning of Sunday's game but also said he doesn't "feel like it's a big deal."
Morton, 36, is 1-1 with a 5.40 ERA in four starts this season. He went 16-6 with a 3.05 ERA and a career-best 240 strikeouts last season, when he was an All-Star and finished third in the AL Cy Young award voting.
To replace Morton on the active roster, the Rays reinstated left-handed reliever Jose Alvarado from the paternity list.