The Braves made the move Sunday after Beachy left Friday night's game against the Phillies with the injury. The rookie is 1-1 with a 3.45 ERA.
The 34-year-old Proctor was 1-0 with a 1.06 ERA and three saves in 14 games with Gwinnett. He had a 6.35 ERA in six games with Atlanta last season.
The Braves plan to make another move to fill Beachy's spot in the rotation Wednesday in Arizona.
Proctor was released by the Braves on March 27. The right-hander signed a minor league deal with the team April 3.