Crain, who hasn't pitched since April 20, said he was going to refrain from activity until Tuesday, when the White Sox begin a three-game series with the Indians. He said he injured his oblique doing twists in the weight room.
The 30-year-old right-hander said he was hopeful he'd be able to return from the DL on May 5, the first day he's eligible.
"We're shooting for there. I think we should be ready by then, depending on what they have me do," Crain said. "I hope it'll give me plenty of time to let it rest all the way and clear it up so it doesn't come back."
Crain, who has a 2.57 ERA over seven innings in six appearances this season, previously recovered from a strained right oblique during Spring Training.
"One side, I can get through it better and don't miss any time and everything was going well," Crain said. "Then, after I pitch I was doing some twists in the weight room and the other side goes, so it's pretty frustrating."
White Sox manager Robin Ventura said right-handers Nate Jones and Zach Stewart would move up in the bullpen to help replace Crain.