Bemboom, who was called up from the minors last week, was injured when he blocked a pitch in the fifth inning.
He was removed from the game and replaced by Travis d'Arnaud.
"I just went down in an awkward position and felt a little instability in my knee,'' Bemboom said. "It's crazy. I've made that move a thousand times before."
Bemboom doubled for his first major league hit and RBI in the second inning, accounting for the only run of the game.
He singled to left field in his second at-bat in the top of the fifth inning.
The Rays already are without regular starting catcher Mike Zunino, who went on the injured list last week with a quad injury that is expected to keep him out four to five weeks.
Information from the Associated Press was used in this report.