Wells was placed on the 15-day disabled list Saturday; also on the DL is right-hander Jeremy Accardo, who is suffering from tightness in his right forearm.
The reliever was 0-3 with a 6.57 ERA and four saves in 16 games for the Blue Jays.
"There's no use complaining because that won't help," manager John Gibbons said. "We'll try to play our best with the players we have. That's all we can do.
"If this job was easy, it wouldn't be any fun."
With a runner on first base, Cleveland's Franklin Gutierrez hit a fly ball to shallow right-center. Wells raced in and caught the ball inches above the ground, then rolled over twice and remained in a kneeling position.
"It didn't feel good then and as the night went on it gradually got worse," Wells said. "I felt something grab in my right hamstring just before the catch. I guess that will be healed in plenty of time before I'm ready now."
The center fielder got to his feet, but remained bent at the waist with his right hand holding his right thigh as head trainer George Poulis came out to attend to him. Wells walked back to the dugout.
"I want to stay with the team and give my support," Wells said before Saturday's game. "I'm a part of this team, though for a while it's going to be as a cheerleader."
Information from ESPN the Magazine senior writer Buster Olney and The Associated Press was used in this report.