Peralta suffered the injury on Saturday and underwent an MRI. Mozeliak said the initial results were "not positive," saying early indications are that Peralta has a torn ligament.
"We have some history with this with Yadi [catcher Yadier Molina]," Mozeliak said. "We've got to determine what this next step looks like."
Peralta said Molina, who had two thumb operations in the offseason, advised him that getting the surgery out of the way rather than attempting to manage the injury could be the preferred course of action.
"He says it's good to do the surgery. Better to do it now than try to wait longer,'' Peralta said Tuesday. "If I do it now, I'll be ready for June or something like that.''
Peralta's second opinion, originally scheduled for Tuesday, was rescheduled for Wednesday.
The 33-year-old batted .275 with 17 home runs and 71 RBIs last season.
Mozeliak said the Cardinals will wait for the results of Peralta's second opinion before deciding whether to pursue outside help at shortstop.
"The outcome of the second opinion will dictate whether we have to look outside," Mozeliak said. "Right now, it would be all hands on deck unless there was an outside solution we would consider."
Jedd Gyorko, who hit 16 home runs with 57 RBIs for the Padres last season, started at shortstop Monday against the Mets. Gyorko played 29 games at shortstop last season in San Diego.
Gyorko said his time at shortstop last season will help him in this situation.
"I'm glad I was able to get those games in because I'm way more comfortable over there than I was before. I think I can handle it. I'm looking forward to the challenge," he said.
Peralta said his thumb felt the same as it did a day earlier, and he didn't appear overly worried about the exam. His biggest concern was gripping a bat. He left the stadium holding several items in his left hand.
"That doesn't mean I can swing,'' Peralta said. "It's different when you swing.''
Peralta was injured making a routine play -- diving for a ball during an exhibition game Sunday.
"When I got the ball, right away I felt something bad in my thumb,'' Peralta said. "I didn't think it was anything serious at the moment, but after the game, I cooled down and that's when I started to feel more pain.''
The Associated Press contributed to this report.