Wainwright is 17-7 with a 3.08 ERA this season.
"He gets better as the game goes, he goes deep in games, he's a big-game pitcher," Shildt said before the Cardinals game on Thursday.
Wainwright has won 10 of his last 11 decisions this season with 11 quality starts during that span.
The 40-year-old righthander is no stranger to the postseason with 28 appearances throughout his career, including earning the save in the World Series clincher against the Detroit Tigers in 2006.
Wainwright has a 3-5 record in 11 postseason starts and will have plenty of backup if needed.
"Everybody will be ready to go for Wednesday," Shildt said. "We have two full days off, so it will be all hands on deck."