The team did not announce a specific injury for either player and did not immediately return a call from The Associated Press.
Peterson, a 13-year veteran in his third season with Atlanta, played four games, including Monday's 45-16 loss at New Orleans, in place of injured Stephen Nicholas.
Hayden played in eight games, but not since helping the Falcons beat Tennessee in Week 11. A second-round draft pick by Indianapolis in 2005, Hayden spent six years with the Colts. He had two interceptions and 22 solo tackles this season.
Peterson had 12 solo tackles and one interception.