Harper sustained the thumb injury when he was hit by a 97-mph fastball in the fourth inning of the Phillies' 4-2 win over the San Diego Padres on Saturday in San Diego.
The Phillies placed Harper on the 10-day injured list on Sunday. Outfielder Mickey Moniak was called up from Triple-A Lehigh Valley and filled Harper's roster spot.
Harper is hitting .318 with 15 home runs and 48 RBIs through 64 games this season. The two-time National League MVP sustained a torn UCL in his right arm in mid-April.
The Phillies claimed outfielder Oscar Mercado on Monday off waivers from the Cleveland Guardians.
The Phillies will host the Braves at 7:05 p.m. EDT Tuesday at Citizens Bank Park in Philadelphia.