In a police report released on Tuesday, Officer Christopher Blaise of the Atlanta police department said Abraham "had a strong odour of alcoholic beverage coming from him, his speech was extremely slurred, his eyes were bloodshot and he was unsteady on his feet" when he was arrested on two misdemeanour charges of obstruction.
Fulton County jail records showed Abraham was released from custody Tuesday at 1:24 a.m. on a $7,000 total bond, or $3,500 for each charge.
The arrest of Abraham, the team's top pass rusher, came one week after running back Michael Turner's drunken driving arrest. Turner, also charged with speeding, was allowed to play in Sunday's 27-3 win in San Diego.
The Falcons are off on Tuesday and there was no word from the team on Abraham's status for Sunday's game against Carolina.
Falcons spokesman Reggie Roberts said Tuesday he did not expect a comment from the team on Abraham's arrest before coach Mike Smith has his normal news conference on Wednesday.
The Falcons said late Monday the team was gathering more information on the incident.
Abraham's arrest came after Atlanta firefighters and police responded to a report of a female threatening to jump from a hotel window Monday night, according to Officer K. Y. Jones.
Officers were moving people away from the scene when Abraham entered the taped-off area.
Blaise said firefighter Jeff Schultz said he asked Abraham to leave at least three times. Blaise said he and a hotel security officer also asked Abraham to remain behind the tape.
Blaise said Abraham "argued with me, stating that he lived at the location and that he owned three condos there." Blaise said he told Abraham other residents were patiently waiting behind the line. Blaise said Abraham continued to argue and was arrested after being asked "at least five more times" to move behind the taped-off area.
Abraham was charged with obstruction of police and obstruction of firefighters.
Jones said the woman did not jump.
Abraham, 34, is the NFL's active career leader with 114 sacks, including two in the Falcons' 3-0 start. He led the team with 9 1/2 sacks last season and remains a key starter.
Abraham, a free agent after last season, signed a three-year, $16.72 million contract to remain with the Falcons. He spent his first six NFL seasons with the New York Jets. He set a career high with 16 1/2 sacks with Atlanta in 2008.