The 25-year-old, two-time All Star said he's had the soreness for a few days but isn't concerned.
"It's the first offseason where I didn't play winter ball. I knew it would take longer to get ready," Andrus said, adding that he'd play through the pain if it was the regular season.
Said Rangers assistant general manager Thad Levine: "We think it's a result from the amount of throwing he's done early in camp. We're just going to try to knock it out early in camp rather than continue to play him every day and not give him a chance to recover."
Levine said Andrus has not received an injection for the pain.
Andrus played in the team's first two spring games, but the team decided to shut him down after an uncharacteristic throwing error on Friday.
"I think he'd like to play through it and I think we took matters out of his hands," Levine said. "It didn't seem to be taking care of itself without attention.
"Once we saw that [throw], we decided we'd try to address this head-on instead of while he was continuing to play."
Andrus has a career .274 batting average and 165 steals.