The 32-year-old was eligible to come off the disabled list when the Braves opened a three-game series against the Giants at AT&T Park on Friday. Garcia's return was first pushed back in order to give him additional time to heal with the hope that he would be back by Monday when Atlanta starts a series against the Angels.
Instead, Snitker said Garcia will back June 2 when the Braves open a three-game set against the Reds in Cincinnati.
"He's going to play some games and there's off-days built in and all of that," Snitker said. "Just to make sure everything's good."
Garcia has responded well to treatment so far and Snitker said the Braves don't want to rush him back too soon given the nature of the injury. Specifically, the concern is over Garcia's initial burst and his ability to round the bases.
"I'm going through it right now so I know the Achilles thing," Snitker said. "That's such a fragile part; we just want to make sure he's sound and get him up to nine innings. He was moving around good when we left but it will be different when you hit a ball and come out of the box and everything. We just want to make sure everything's tightened up."
Garcia is expected to play three or four games while out on his rehab assignment with Gwinnett.
When Garcia returns, Snitker said it's likely he will be in a platoon situation at third base with Rio Ruiz. Ruiz has started eight of nine games, including Friday in San Francisco, since being called up from the Minors on May 18.
"Rio's here and he's doing pretty good," Snitker said. "We'll probably, I don't know, right now probably split it up a little bit and try to get a really productive position out of both of them."
Michael Wagaman is a contributor to MLB.com and covered the Braves on Friday. This story was not subject to the approval of Major League Baseball or its clubs.