Moustakas was taken out of Monday night's 6-3 loss to the Tigers in the ninth after re-injuring his left groin while sliding at second base in the sixth inning. He stayed in the game until after he struck out in the eighth.
"That's when I saw it and noticed the grimace on his face. I said that's it," Yost said.
Moustakas sustained the injury in Sunday's game at Cleveland, the day after a 14-inning marathon win over the Indians.
"I tweaked it coming in on a play and didn't think too much of it," he said, "and then [Monday] on the slide I kind of tweaked it up again, so the skip says no reason to get out there again."
Hosmer sustained a slight tear in his right rotator cuff last Thursday on a fielding play at Detroit. He hasn't played since.
Moustakas, after a fast start, finishes with a .242 average but his 20 home runs and 73 RBIs as of Monday were second on the team only to Billy Butler's 29 homers and 107 RBIs.
Hosmer, following a sensational rookie season, struggled this year. His numbers include a .232 average, 14 homers and 60 RBIs.