Wells has a strained right forearm and Cashner a mild strain in the back of his right rotator cuff, Major League Baseball's official website (www.mlb.com) reported.
"We're not going to put a time frame on any one of them because we're going to be careful in April," Cubs General Manager Jim Hendry told reporters. He added it would be at least two weeks before they picked up a baseball.
The right-handed Wells posted an 8-14 record while starting 32 games last season. Cashner, also a righty, went 2-6.
"I'm not going to rush anything and make sure I'm completely healthy," Wells said. "When I come back and make my next start, I'm going to be 120 percent."
(Reporting by Gene Cherry in Salvo, North Carolina; editing by Rex Gowar)