Crawford has been sidelined since April 28 with a torn oblique - his fifth DL stint since 2012.
Beachy was sent down after going 0-1 with a 7.88 ERA in two starts. The right-hander made his debut with the Dodgers on July 11, losing 7-1 to Milwaukee.
Crawford, a four-time All-Star with Tampa Bay, is hitting .288 with 15 homers, 80 RBIs and 38 stolen bases in 236 career games with Los Angeles.
Beachy, who went 14-11 with a 3.23 ERA in 46 career starts for Atlanta, had been sidelined since August 2013 following a second elbow ligament replacement surgery.