The Cardinals limited Goldschmidt's throwing during the start of spring training, and he made his first two exhibition starts as a designated hitter. He has not played since Sunday.
Cardinals manager Mike Shildt said Wednesday he expected Goldschmidt to miss a couple more games.
"He's had off-and-on discomfort," Shildt said.
Goldschmidt, a six-time All-Star and three-time Gold Glove winner, is hitting .300 with two homers in 20 spring training at-bats.
Goldschmidt, 32, hit .260 with 34 homers and 97 RBIs last year for the NL Central champions after the Cardinals acquired him in an offseason trade with Arizona. His batting average was more than 30 points below his career average.
Right-hander Miles Mikolas was scheduled to play catch on Wednesday as part of his rehabilitation from a flexor tendon injury in his throwing arm. The 2018 All-Star received a platelet-rich plasma injection on Feb. 18 and is expected to miss the first month of the season.