Garza first experienced soreness after a side session on May 19, and he missed his Sunday start in Boston.
The Cubs called up outfielder Luis Montanez from Triple-A Iowa and made him the starter in right field Tuesday. He went 2-for-4 with two runs and an RBI as the Cubs routed the Mets 11-1.
"I'm not happy to go on the DL," Garza said. "I fought it, but there is nothing I can do about it. I'd rather be out there 100 percent than put myself in jeopardy or put the team in bigger jeopardy. I'll try to get healthy, come back in a start or two and get after it."
Garza said he had the same type of pain before in his career but was always able to pitch through the discomfort.
"This one is right on the spot that gets used a lot," Garza said. "That is probably why it is so naggy. But structurally we are happy. I'm not happy but it's a great relief as to what it could have been."
Garza was concerned about ligament damage.
"The good news is there is no damage to the ligament," Cubs general manager Jim Hendry said. "The injury was in the area where potentially you could have thought there was some damage to the nerve, which there wasn't. So it's like a deep bone bruise with some inflammation around the joint."
Garza will wait for a go-ahead from team doctors before he picks a ball up again. He and the team hope he can return the weekend of June 3 in St. Louis.
In his first season with the Cubs, Garza is 2-4 with a 3.72 ERA. Going into Tuesday's games, he was tied for sixth in the National League with 68 strikeouts.
Montanez was the Cubs' first-round pick and third overall in 2000, but he's never played for the Cubs in the majors. After playing the last three seasons with the Orioles, Montanez signed a contract with the Cubs during the winter.
The 29-year-old was hitting .369 with five home runs and 43 RBIs at Iowa.
To make room for Montanez on the 40-man roster, right-hander Brian Schlitter was transferred to the 60-day disabled list Tuesday.
In other Cubs injury news:
Marlon Byrd visited a specialist about the facial fractures he suffered when he got hit in the face Saturday night. He was told he can't do any activity other than walking for one to two weeks. "He's making solid progress," Hendry said. "The bruising in the retina area was subsiding some, which is good. The healing process has started. He will continue to see doctors at Northwestern as the week progresses."
Geovany Soto has recovered from a left groin strain. He will play for Double-A Tennessee on Thursday and Friday. If he comes out of those two games physically fit he will return to the Cubs on Saturday.
Jeff Baker is day to day with a strained left groin. Manager Mike Quade said he would try to stay away from using him against the Mets on Tuesday.
Dr. Lewis Yocum confirmed the Cubs' diagnosis of a strained rotator cuff for Andrew Cashner. He won't pick up a baseball for two weeks and his rehab should be six to eight weeks, similar to the one he started on April 8 before re-injuring himself.
Randy Wells returned to the Cubs on Tuesday after completing his rehab and his final start at Triple-A Iowa on Sunday. He will start against the Pirates on Saturday.
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.