Miami right-hander Tom Koehler struck out Upton to end the second inning of Tuesday night's game. Upton shook his left hand in apparent pain while walking back to the dugout.
The Braves say Upton's status is day to day.
Reed Johnson took over for Upton in centre field to open the third inning.
Upton is hitting only .176 with eight homers, 19 RBIs and seven stolen bases.
Manager Fredi Gonzalez said before the game outfielder Jordan Schafer would be available off the bench. Schafer has not played since fouling a ball off his right ankle on Wednesday.