Wren, who took up the post in 2007, has been dismissed after the Braves' hopes of a place in the post-season were dashed with a 10-2 loss to the New York Mets.
That loss sealed a three-game series sweep for the Mets and more importantly saw the Braves' record drop to 76-79, eight games behind the wildcard places in the National League with only seven left to play.
The 56-year-old Wren will be replaced in the interim by John Hart, who is said to be a close friend of franchise president John Schuerholz.
Hart has served as a general manager with the Cleveland Indians and the Texas Rangers and had been working as a pundit for the MLB television network.
In addition Hart will reportedly form part of a three-man committee, along with Schuerholz and ex-Braves manager Bobby Cox, to find Wren's permanent replacement.
Atlanta wrap up a disappointing campaign with four home games against the Pittsburgh Pirates before heading on the road for three matches with the Philadelphia Phillies.