Odorizzi was struck by a ball hit at 103.2 mph off the bat of Kansas City Royals outfielder Alex Gordon.
Righty Jorge Alcala replaced the All-Star hurler.
Odorizzi was diagnosed with an abdominal contusion, according to Betsy Helfand of the St. Paul Pioneer Press.
"Just chatting with him right now, he's OK, he's pretty sore obviously," manager Rocco Baldelli said postgame, per Fox Sports North. "He's got a pretty good mark visible from across the room right there on his abdomen.
"It looks like, from everything we've seen so far, that he was able to avoid serious injury, which is really all we're caring about at this point."
Odorizzi owns an 8.10 ERA this season across three starts after posting a 3.51 ERA in 30 games in 2019.