The National Weather Service said there was a "threat for severe thunderstorms producing tornadoes, strong winds, large hail, and additional flash flooding" on Tuesday night.
Michael Wacha (3-1), who had been scheduled to start for St. Louis on Tuesday, will pitch the game against Kansas City's Brad Keller (2-5).
Homer Bailey (4-4), the Royals' starter Tuesday, will pitch the night game against Adam Wainwright (3-4).
St. Louis has lost seven of 10 games. Kansas City won Sunday to stop a four-game losing streak.