The Cincinnati police department admitted it was entirely at fault for the incident and told NFL Network that the department had apologized to Jones and Lewis.
Cincinnati police chief Tom Streicher said at a news conference Monday that the police department made a mistake and Jones did nothing wrong. The chief called the episode unfortunate.
According to the police report, officer Amy Moore said Jones accidentally drove his silver Jaguar over a curb near Great American Ball Park. The streets downtown were crowded with fans leaving the Bengals game -- which ended about 90 minutes earlier -- and others going to the Reds' evening playoff game against the Philadelphia Phillies.
Officer Barbara Maleski obtained Jones' Georgia driver's license, and a dispatcher told her there was outstanding warrant for the player. Then the dispatcher corrected herself, but because of noise in the area, Maleski didn't hear the dispatcher say the warrant was for someone else.
Jones was taken into custody and remained in a police car while officers determined there was no warrant for his arrest. Witnesses took cell phone photos and shared them on social media sites with captions claiming -- incorrectly -- that Jones had been arrested. He later was driven back to his car and released.
Jones' agent, Thomas Hunter, released a statement saying "Adam has accepted the police chief's sincere apology and wants to allow the police department to put this behind them ... Adam would like to thank the media for coming to his defense and helping him flush out the truth, he is also grateful for the team standing behind him."
Jones has a history of off-the-field problems and was out of football last year because of those issues. Jones had six arrests and a dozen incidents involving police intervention, leaving his career at a crossroads.
Jones played well with Cincinnati during the preseason and won the third cornerback job. He has eight tackles and one interception in four games this season.
The Associated Press contributed to this report.