Morgan (shoulder) made the second appearance of his rehab assignment Tuesday with Triple-A Columbus, recording one out while giving up two earned runs on zero hits and two walks.
The Guardians placed Morgan on the 15-day injured list Wednesday with right shoulder inflammation, Joe Noga of The Cleveland Plain Dealer reports.
Morgan (1-0) allowed an unearned run on one hit and struck out two without walking a batter to earn the extra-inning win over the White Sox on Wednesday.
Morgan has allowed one run on one hit and struck out three over three Cactus League innings.
Morgan (4-2) allowed three runs on three hits and a walk over one-third of an inning to take the loss Monday versus the Astros.
Morgan (4-1) allowed a hit and struck out two over a scoreless inning to earn the win Thursday over the Royals.
Morgan (2-1) allowed one run on a hit and two walks in one-third of an inning, taking the loss Thursday versus the Twins.
Morgan (2-0) allowed two unearned runs on one hit and struck out one in one inning to earn the win Saturday over the Angels.
Morgan has allowed three earned runs on five hits and no walks while striking out four over three innings in three Cactus League games.
Morgan (5-3) allowed a hit in a scoreless inning to pick up the win Monday over the Royals.