Wren has been the team's general manager since October 2007. The Braves are in second place in the NL East, but they only have a 76-79 record and are 15.0 games behind the Nationals.
Atlanta was eliminated from the Wild Card race with Sunday's loss and has lost eight of its last 10 games.
"It's disappointing," Wren told The Associated Press on Sunday. "I think we had a club we thought could go into the postseason and have a good chance because of our pitching."
During Wren's tenure, the Braves only made the playoffs twice, winning just one game. Bob Nightengale of USA Today reports that Wren is the first Braves' GM or manager to be fired since 1990.
- Paul Palladino