A three-time Gold Glove award winner, Wells was injured when he jumped against the outfield fence to catch a deep drive by Rays outfielder Ben Zobrist in the sixth, helping preserve Brandon Morrow's no-hit bid.
Morrow gave up a single to Evan Longoria with two outs in the ninth inning as the Blue Jays won 1-0.
Wells stayed down for a moment after making the catch, then jogged gingerly off the field.
X-rays did not reveal any fractures but Wells will undergo further tests Monday.
"We were running in and I could feel it wasn't in place anymore," Wells said. "I was hoping it would pop back in as I was running in but it didn't, so they told me I had to come out."
Wells, who hit an RBI single in the first, is batting .274 with 22 home runs and 60 RBIs. Travis Snider batted for Wells when his spot in the order came up in the bottom half of the inning.
Information from The Associated Press contributed to this story.