They will not pick up a ball for at least two weeks, Hendry said, and they will be re-evaluated at that point.
"It could've been a lot worse -- I could've been out the rest of the year," Cashner said. "It is what it is, and I'll get strong and get back out there when I can."
The Cubs don't need another starter until Sunday in Milwaukee and are expected to call up right-hander Casey Coleman from Triple-A Iowa. They also will look at lefty James Russell as another option, and he could start on Tuesday in Houston.
"We'll find a way to get through it," Hendry said.
Neither Wells nor Cashner felt any discomfort in Spring Training. Wells started on Monday and threw 99 pitches over six innings against the D-backs. He said he had some soreness in his forearm on Tuesday. There is nothing wrong with his elbow, Hendry said.
"The MRI showed nothing structural, the ligament is fine, and I just have a strain in the forearm and the flexor there," Wells said. "I'm just going to take some rest and time and come back stronger."
Wells, who threw 194 1/3 innings last season, has been one of the most durable pitchers on the Cubs last season.
"It's one of those freak things," Wells said. "I'm not going to rush anything and make sure I'm completely healthy. When I come back and make my next start, I'm going to be 120 percent."
Cashner made his first Major League start on Tuesday and gave up one run on two hits, including a solo homer by Arizona's Ryan Roberts, over 5 1/3 innings. He had gone to a three-ball count on two batters, including Willie Bloomquist, who drew a walk with one out in the sixth. Cashner said he felt the discomfort on the last two pitches to Bloomquist.
"We were counting on those guys, absolutely," Cubs manager Mike Quade said. "Now we're counting on them to get back as quick as they can and come back healthy."
Quade remained optimistic.
"In this day and age when you hear about people who get shut down for a year, this could be a lot worse," Quade said. "I'm expecting three, four weeks and we're back in action, and that's a lot better than three or four months.
"It's a long season, and those two guys will be back to help us."