Right-hander Evan Phillips was called up from Triple-A Gwinnett to take his place.
Fried (1-3) started a 7-2 loss to Milwaukee on Thursday, going three innings and allowing four runs on four hits and three walks.
Braves manager Brian Snitker said the team is trying to get ahead of the injury by placing Fried on the disabled list now instead of letting the issue linger and potentially get worse.
Phillips' most recent stint at Gwinnett lasted two days. He appeared in Tuesday's loss to the Yankees, allowing two runs in 2 1/3 innings in his major league debut and was sent down the next day.