Rodriguez pitched four innings Saturday night against Colorado before leaving with the injury. He allowed two runs, one earned, on five hits. He struck out five and walked three.
"He was a little sore this morning," manager Cecil Cooper said. "It's a disappointment because he was pitching so well. It had bothered him the last couple of starts and [Saturday] he didn't wrap it like he had been."
Rodriguez is 1-0 with a 2.31 ERA in three starts.
"It's disappointing," Rodriguez said through an interpreter. "But it's better this way. I don't want to make it worse."
General manager Ed Wade did not think the injury would be a long-term problem.
"I've had no indication from [Astros head trainer] Dave Labossiere [on that]," Wade said. "He's been pitching great and navigating through whatever mild discomfort he had so our anticipation is after 15 days he'll be ready to go."
Byrdak had a 3.68 ERA in seven appearances for Round Rock. He was 3-0 with one save and a 3.20 ERA in 39 appearances for Detroit last season. He's 4-5 with three saves and a 5.50 ERA in 144 career appearances.
Cassel is 1-1 with a 2.50 ERA in three starts for Round Rock this season. His first year in the major leagues was 2007, when he went 1-1 with a 3.97 ERA in six games with San Diego.