Brewers manager Ken Macha said Hart, the right fielder, had a sore lower back and Braun, the left fielder, had a sore wrist.
Hart came out of Sunday's game against the Houston Astros in the top of the sixth inning. He took part in batting practice, but told Macha that he couldn't go.
However he did come on as a pinch hitter for reliever John Axford in the ninth inning. Hart grounded out to third in his only at-bat.
Braun appeared to hit his left wrist against Astros first baseman Brett Wallace in a play at first in the bottom of the fourth.
Braun has a left wrist strain and contusion. He is listed as day-to-day.
Information from The Associated Press was used in this report.