Braun left Saturday's 5-3 win over the Cubs after the eighth inning with a slight chest muscle strain.
Braun was also involved with Segura's injury. The slugging outfielder was swinging his bat on the dugout steps in the first inning when he accidentally hit Segura in the face as the shortstop was coming up behind him.
Segura had a partially closed right eye and bruised right cheek.
Manager Ron Roenicke was unsure how long either player might be out, though he didn't expect it to be long.
Milwaukee had just two available bench players with catcher Martin Maldonado still suspended for his part in a brawl last week.