The 36-year-old Moylan, who spent his first seven seasons with the Braves, is looking for his first major league appearance since 2013 with the Dodgers.
Moylan, who has endured back, rotator cuff and two Tommy John surgeries in his career, was 2-0 with a 3.14 ERA and six saves in 27 games with Gwinnett. He is 21-9 with a 2.80 ERA in 309 career games with the Braves and Dodgers.
Moylan had three seasons with at least 80 appearances as a top setup reliever with the Braves from 2006 to 2012.
Rookie right-hander Jake Brigham was optioned to Gwinnett before Sunday's game against Arizona. Brigham allowed two runs without recording an out in Saturday night's 8-4 loss to the Diamondbacks.