Lee might be able to return as soon as he's eligible to come off the DL, general manager Ruben Amaro Jr. said late Tuesday.
"It's never good news when you lose one of your No. 1 pitchers, but it's pretty mild," Amaro said.
Amaro didn't offer a timetable on how long Lee may be out.
"We just don't know yet," he said. "It could be two weeks. It could be three weeks. It could be four weeks. Who knows. It could be 30 weeks. We think it will be shorter. It's a pretty mild strain. ... We just have to be really cautious with him."
When Lee underwent an MRI on Tuesday in Philadelphia, there were concerns the left-hander might become the latest major league pitcher to be sidelined by a serious injury. More than a dozen have already have undergone Tommy John elbow surgery this year, including All-Stars Jose Fernandez, Patrick Corbin, Josh Johnson and Matt Moore.
"The Tommy John thing is not what it is," Lee said. "That was good."
Lee pitched 6 2-3 innings in a win over Cincinnati on Sunday. He said his elbow began to bother him after he threw a career-high 128 pitches in an 11-hit, complete-game loss against the Braves on April 16.
"After the game it was pretty sore," he said. "We started doing some treatment on it and it acted like it was doing a little better, and this past start I started feeling it the last couple of innings just about every throw, and obviously it was pretty sore the next day.
"It was definitely concerning that it was there on every throw. With as much season as we have left, I didn't feel that I could keep pitching."
Amaro said he wasn't sure what caused the injury.
"He's pitched a lot, but his arm has never really been hurt," Amaro said. "He's had abdominal issues, but never an arm (injury). So he's perplexed. He doesn't like to be hurt. He actually fought us a little (about going on the disabled list) until he got the MRI and we told him the MRI results."
Lee rejoined the Phillies in Miami after he was diagnosed with a Grade 1/2 strain of his flexor tendon.
"That's better news than the other," teammate A.J. Burnett said. "You're happy for that."
The 35-year-old Lee is 4-4 this season with a 3.18 ERA in 68 innings. He'll rest for a week and is expected to resume throwing after that.
"We don't really know until we get there, but hopefully in a week it's gone and I start playing catch, and in another week I'll start being in games," Lee said.
The Phillies recalled OF/1B Darin Ruf from Triple-A Lehigh Valley to take Lee's place on the roster. Ruf is batting .265 in nine games after missing the first month of the season with a strained oblique.
Amaro said right-hander David Buchanan, who had a good spring for the Phillies, was "the most likely choice" to replace Lee in the rotation, but he said "we're still trying to figure it out."
Lee has thrown more than 200 innings every season since 2008, when he was the AL Cy Young Award winner.
Information from ESPN.com's Jayson Stark and The Associated Press was used in this report.