Atlanta made the moves before Friday night's game at Arizona.
Minter is 0-4 with a 9.82 ERA. The lefty had three saves in four opportunities after replacing injured closer Arodys Vizcaino early in the season, but right-hander Luke Jackson had taken that role in late April.
Venters, who had been out since April 15 with a right calf strain, and Jackson could be used in save situations, manager Brian Snitker said.
"Mix and match," Snitker said. "It might be Jonny. He's been through all that. We'll just kind of play it by ear. Maybe two guys that split the ninth inning. We could do that, also."
The 34-year-old Venters made seven scoreless appearances during a rehab assignment at Triple-A Gwinnett after giving up six runs in 2 2/3 innings with the Braves this season. Venters had three saves last season, two with Atlanta and one with Tampa Bay.
Jackson is 2-0 with a 2.65 ERA and two saves in three chances this season. He gave up a game-tying homer with two outs in the ninth inning of a 3-2, 10-inning loss to Arizona on Thursday. Minter gave up a walk and two singles to take the loss.