Manager Brian Snitker told reporters that the hope is that Smyly will miss only one start.
The Braves recalled right-hander Kyle Wright from their alternate training site to start Friday's game. Wright will be making his 2021 debut after going 2-4 with a 5.21 ERA last season.
Smyly last pitched in Sunday's 7-6 loss to the Philadelphia Phillies, a game that was decided by a home-plate review of an Alec Bohm slide. The 31-year-old pitcher is 0-0 with a 5.73 ERA in two starts this season.
Infielder Johan Camargo was also called up by Atlanta.
ESPN's Jesse Rogers contributed to this report.