The Falcons also waived linebacker Joplo Bartu.
Bryant was injured during Wednesday's practice. Head coach Dan Quinn Graham did not immediately rule Bryant out for Sunday's game against the Minnesota Vikings. Bryant is 14 of 18 on field goals this season.
Graham was originally signed by the New Orleans Saints as a college free agent following the 2000 NFL Draft out of Virginia Tech. He has spent time with nine different teams, including his latest stop with the Saints in 2014. Graham made the Pro Bowl in 2005 when he played for the Cincinnati Bengals. He has played a combined 173 games over 14 years and has made 266 of 311 field goals.
Bartu was originally signed by the Falcons as college free agent following the 2013 draft out of Texas State. In two NFL seasons, he has appeared in 32 games while making 27 starts and totaling 192 tackles, 4.5 sacks, two forced fumbles and two passes defensed.