Miller suffered a right elbow contusion in his previous start. Carl Crawford lined the second pitch off the game off Miller's right elbow, and he immediately left the game.
The rookie had originally been scheduled to face the Pirates on Tuesday, but the Cardinals have an off-day Monday, which allowed them to start Adam Wainwright in Tuesday's series opener on normal rest. Lance Lynn is scheduled to throw on Thursday.
The right-hander has been a key part of the Cardinals rotation this season, going 11-7 with a 2.89 ERA in his first 22 starts. Miller is considered a strong contender in a deep NL Rookie of the Year race.
The upcoming series is important for both teams. The Cardinals enter Monday trailing the Pirates by three games in the NL Central, and the Cincinnati Reds are close by, trailing the Cardinals by two games.