Gyorko left Monday's game in the seventh inning with a strained right hamstring. Greg Garcia will fill in at third base.
Gyorko batted .272 with 20 home runs and 67 RBIs last season but missed 17 games in early September because of the same injury.
"That heightened our concern," manager Mike Matheny said. "But it was pretty clear when we came off the field that it would take a little time. How much time, we're not sure."
Bader is an outfielder who was named the Cardinals' minor league player of the year last season. He had been assigned to Memphis in the Pacific Coast League, though the Triple-A season has yet to begin. Bader batted .235 with three home runs in 32 games with St. Louis last season after hitting .283 with 20 homers at Memphis.
"He was swinging the bat as well as anybody," Matheny said. "He had a good enough swing to make the club but (the decision) was more about flexibility than anything else.
"We wanted him to be ready in case something happened."
Matheny also said that injured pitcher Adam Wainwright worked out Tuesday without issue. The right-hander is coming back from a hamstring injury and is set to come off the DL on Thursday for the home opener against Arizona.