The Cardinals made the moves Sunday after their 5-3 win over Philadelphia.
The right-handed Wacha has a stress fracture in his pitching shoulder. He is 5-5 with a 2.79 ERA for the defending NL champions.
Garcia has re-aggravated his surgically repaired left shoulder. He is 3-1 with a 4.12 ERA.
St. Louis general manager John Mozeliak said it was too early to determine when the players will return. He said the team was aware of Garcia's soreness, but the Wacha ailment took him by surprise.
"This was a little shocking to all of us," Mozeliak said. "In terms of how long he's going to be out, I don't know that. We're going to give him a couple weeks and see how he is and then re-evaluate."
Wacha said he has not felt right the last couple starts.
"It's just tightness, it just takes a little bit longer to warm up," Wacha said. "It's a little discomfort, something I'm not used to."
Garcia missed all but nine starts last season and underwent surgery to repair a torn labrum. He could be forced to undergo a third surgery.
Wacha was the MVP of the NL Championship Series as a rookie last season throwing 13 2/3 shutout innings against Los Angeles.
Garcia went 26-15 between 2010 and 2011 before suffering shoulder injuries the next two seasons.
Mozeliak indicated that Carlos Martinez will likely remain in the starting rotation. Martinez went five innings and picked up the win in Sunday's 4-1 victory.