Wells was hurt during an at-bat in the fourth inning. The 32-year old got only a few feet out of the batter's box on his grounder to third baseman Brent Morel. He quickly doubled over and was joined on the field by Angels manager Mike Scioscia and trainer Rick Smith.
It's Wells' first DL stint since he broke his wrist in 2008.
On Tuesday, the Angels recalled Reggie Willits from Triple-A Salt Lake to fill Wells' roster spot.
The Angels are a bit stretched for outfield depth, without a reserve outfielder -- other than 37-year-old designated hitter Bobby Abreu -- on their 25-man roster.
"That's a blow for us right now," Scioscia said.
"Vernon was starting to come alive, swinging the bat much better. We definitely talked about the importance of getting him back into his game and that's obviously going to be pushed back a little bit right now."
Wells said White Sox catcher A.J. Pierzynski asked him "if that was my leg that popped," after he pulled up just a few steps outside the batter's box following his fourth-inning groundout.
"There's never a good time to have these," Wells said. "The most frustrating thing is just not being out there. Good or bad, whatever your numbers are as an individual, there are still ways to help a team win. It's just frustrating having to sit by and watch."
Wells, who played the first 10 seasons with the Toronto Blue Jays before the Angels acquired him for Mike Napoli and Juan Rivera in January, was off to the worst start of his career. He came into Monday's game batting .179 and just .117 at home.
Mark Saxon covers the Angels for ESPNLosAngeles.com.