Gwinnett County police have told TV-11 Alive in Atlanta that a dog in Babineaux's care died and that they believe he was somehow involved in its death.
According to a report on the NBC affiliate's Web site, police say Babineaux's wife rushed a dog to an animal emergency center, where workers confirmed the dog died.
Georgia law states that felony animal cruelty only applies when someone knowingly and maliciously causes death or physical harm to an animal, the station said.
More details are expected to be made available Tuesday. The Falcons confirmed the arrest in a brief statement released Monday.
"We're aware of the situation and we're in the process of
gathering information," said Falcons spokesman Reggie Roberts.
"Until we have the information we need, we will have no further comment."
Gwinnett County police spokesman Darren Moloney said Babineaux
was arrested early Monday. Moloney did not give further details.
Lt. Derrick Locklear, shift commander for the Gwinnett County
Sheriff's Office, said Babineaux was released just before 8 a.m.
Monday on a $2,300 bond.
Babineaux played in all 16 games and recorded 28 tackles last season.
Information from The Associated Press was used in this report.