Texas general manager Jon Daniels said Wednesday that Jennings will head to the DL on Saturday when the Rangers will call up A.J. Murray from Triple-A Oklahoma to start at Oakland.
Jennings left Tuesday night's game against the Kansas City Royals after throwing his second pitch of the third inning.
"We're going to give him some time to recover," Daniels said. "We don't expect he'll be down long."
Jennings missed nearly three months last season because of a torn tendon in his right elbow while a member of the Houston Astros. He has struggled in his comeback, going 0-5 with an 8.56 ERA in six starts.
"This is another bump in the road," Jennings said.
Jennings' injury is another blow to the Rangers rotation. He will be the team's fourth starting pitcher on the disabled list.
Gabbard may soon return to the rotation. He is scheduled to make a rehab start for Double-A Frisco on Saturday.
Daniels said if Gabbard responds well, he may start for the Rangers in a series the Seattle Mariners from May 5-8.