Cubs general manager Jim Hendry said the two won't throw for two weeks and will be re-evaluated.
"We're going to have to go through some early season adversity here," Hendry said Wednesday.
Wells reported soreness after making his first start of the regular season, a 4-1 win over the Pittsburgh Pirates, on Monday. The injury was diagnosed as a strain in his right forearm.
"There's nothing that's going to stop (Wells) from coming back in a reasonable amount of time," Hendry said. "But we're not going to put a timetable on either one of these guys just because we're going to be careful in April."
Cashner was pulled during the sixth inning of his first career start on Tuesday, a 6-5 win over the Arizona Diamondbacks. He has been diagnosed with a mild strain in the back of the rotator cuff in his right shoulder.
"Obviously, we're going to proceed with extreme caution," Hendry said.
MRI exams on both pitchers did not reveal any structural damage.
"Any time you go get an MRI, you get nervous," Cashner said. "To be out for two weeks, it could have been a lot worse."
Wells and Cashner pitched well in their regular-season starts.
Wells allowed just one run in six innings, striking out six and walking four. He was 8-14 with a 4.26 ERA last season for the Cubs.
"I'm just going to get some rest and take some time and hopefully come back stronger," Wells said. "It's really disappointing. This is a big year for me."
After breaking into the big leagues as a reliever last season, Cashner was impressive in his first appearance after being moved into the Chicago rotation. He had allowed just two hits and one run in 5 1/3 innings against Arizona before being removed because of discomfort.
The right-hander was consistently throwing his fastball in the mid-90s.
"He's a scout's dream," Hendry said. "You're not going to see an easier 97 (miles per hour) than that."
Cubs manager Mike Quade has resolved to remain upbeat.
"It's part of the deal," Quade said. "We're were counting on those guys, absolutely. Now we're counting on them to rehab like a son-of-a-gun and get back as quickly as they can."
Hendry said Wells and Cashner will be placed on the 15-day disabled list before Friday. One of their replacements will be Triple A pitcher Casey Coleman, who likely will start for Wells in Sunday's game at Milwaukee.
Coleman was one of the last players cut by the Cubs during the spring.
"We sent (Coleman) out for exactly this reason," Quade said. "To keep him pitching. If he's sitting here in our bullpen and has only pitched an inning or two, where's he going to be at as far as lengthening him out?"
Coleman pitched in eight games for the Cubs last season, starting eight. He was 4-2 with a 4.11 ERA.
The team has not decided who will start for Cashner on Tuesday at Houston.
"We'll find a way to get through it," Hendry said. "No excuses. Nobody is going to feel sorry for us."