Wellemeyer, on the disabled list with inflammation in his right elbow, hasn't thrown since he cut short a throw last Sunday when he felt something in his elbow. He missed his scheduled start on Tuesday against the Reds and was soon placed on the DL.
Examined by team doctors on Saturday, Wellemeyer was given the go-ahead to begin throwing.
"I'm just going to stay back here and throw," Wellemeyer said. "Hopefully I will be ready for some bullpen [sessions] when they get back in town, and then I will hopefully be ready to go on the next road trip."
The veteran is 7-9 with a 5.67 ERA in 23 games for the Cardinals. He was pulled from the starting rotation and made two relief appearances before being scheduled to return to the rotation when the injury occurred.
Rookie Mitchell Boggs will start Tuesday in Los Angeles in Wellemeyer's place, but the team hasn't announced the plan for the fifth starter's spot beyond that.
B.J. Rains is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.