The team said Wednesday that Punto will have the surgery later this week.
He was injured Saturday on the first day of workouts for position players, then participated in drills Sunday before flying to St. Louis to be examined by the team doctor.
A career .247 hitter, Punto batted .238 in 88 games last season with Minnesota. His best year came with the Twins in 2006, when he hit a career-high .290 and scored 73 runs.
The injury leaves the Cardinals vulnerable at third, where projected starter David Freese came to camp following offseason surgery on both ankles.