The left fielder had the surgery Friday but the team believes the condition was caught early and he could be back before the end of a 15-day DL stint.
Manager Tony La Russa said the team would wait until Monday or Tuesday, hinting that Holliday might even stop by Busch Stadium on Saturday.
General manager John Mozeliak said Holliday would have no baseball activities for five days, and said early indications were positive.
"They're saying it went well," La Russa said. "That's all I know so far."
Losing Holliday for a longer period would be another huge early blow to the franchise, after 20-game winner Adam Wainwright underwent reconstructive elbow surgery early in spring training.
"Wainwright, that's a totally different discussion," Mozeliak said. "Whenever you lose somebody for the entire season, especially of his caliber, you reel from it, but we've all moved on from that.
"You take things in stride. It's disappointing, but in my job you just have to think of what the next move is."
La Russa said he'd likely move Lance Berkman, a switch-hitter who's been more productive batting left-handed in recent seasons, up from fifth to cleanup against right-handed pitchers while Holliday is out.
Albert Pujols said he spoke with Holliday before the laparoscopic procedure and was optimistic he'd be back soon.
"Obviously, his presence is going to be missed," Pujols said. "When you look at that lineup, you're expecting Matt to be there, and he won't be there probably for the next week or so."
Craig, who was batting sixth, and Jon Jay will get the bulk of the playing time. Craig has long been considered one of the franchise's best offensive prospects, but has struggled in a bench role.
"I think that's tough for anybody," Craig said. "We always want to be in the lineup and be playing every day and it's easier to make adjustments. But it's part of my job, and part of the job for all the guys that aren't playing a lot, to be ready."
Craig got work at third base in spring training as a backup option for Freese, who is coming off surgery on both ankles last season.
Craig doesn't care where the Cardinals put him. He started at all four corner positions last year, with 23 of his 27 starts in right field, two in left field and one each at first base and third. La Russa said Berkman would stay in right.
"It's good to be good at a bunch of positions," Craig said. "Then they can put you in the lineup wherever they need you."
Freese batted cleanup once last year as a rookie, going 0 for 4 at Pittsburgh May 9. La Russa batted Freese fourth in spring games when Holliday had the day off.