Wile injured his quadriceps before Sunday’s game against the Cardinals.
In two games subbing for starting punter Matt Bosher this season, Wile punted six times for 290 yards, a 48.3 average.
The Falcons have had Wetzel on and off the 53-player roster this season, but he has yet to play in a game. In his career, Wetzel has played 40 games, with 24 starts, all with the Cardinals.
Atlanta also announced it signed tight end Carson Meier to the practice squad.