Parmelee, who was slated to start in right field against the Indians, was scratched in favor of Matt Carson, who started in right for the fifth time this year.
Parmelee suffered the injury while running down a line drive in the gap while playing right field in Sunday's 8-7 win over the Indians.
"The ball went through those two [in the outfield] and he felt something," manager Ron Gardenhire said. "So he's day to day."
Parmelee has been swinging a hot bat since being recalled from Triple-A Rochester on Aug. 29. He's hitting .349 with three homers and four doubles in 11 games.