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.
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.''
Lee rejoined the Phillies in Miami after he was diagnosed with a grade one/two 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.
Amaro declined to say who will start for Lee on Saturday against the Los Angeles Dodgers.
Lee has thrown more than 200 innings every season since 2008, when he was the AL Cy Young Award winner.