Damon appeared to get hurt while attempting to bunt in the third inning. He had the hand placed on the middle of his bat and it appeared to get partially struck by Brian Duensing's pitch.
"It's very sore," Damon said. "Really tough to squeeze anything. It's pretty bruised. It's just very unfortunate. Hopefully I'll be ready to go as soon as possible."
Matt Joyce replaced Damon defensively in the fifth. The Twins defeated the Rays 4-2.
The Rays said Damon's status is day to day.
Information from The Associated Press was used in this report.