This story has been corrected. Read below.
Jones, who has had a spate of legal troubles, was issued a citation around 2:30 a.m. after the vehicle he was in was pulled over for driving 60 mph in a 45 mph zone on a highway in Cincinnati, State Patrol Lt. Anne Ralston said.
It was originally reported that Jones was arrested; however, in Ohio police officers are directed to issue citations for minor misdemeanors unless the offender needs medical care, can't verify identity or won't sign the citation. A police report obtained by ESPN shows that Jones was issued a citation for disorderly conduct.
The driver was cited for driving under the influence. Both charges are misdemeanors. Jones and the driver were released and have court hearings set for Friday.
Jones' agent and his attorney did not immediately return phone calls seeking comment Monday.
The Bengals are aware of the incident but have no plans to address it publicly at this time.
"As with most situations of this nature, it would be inappropriate for the team to comment until the matter is resolved through normal legal channels," a team spokesman said.
Ralston said Jones said something during the traffic stop that was "likely to be offensive or to cause inconvenience, annoyance or alarm to persons of ordinary sensibilities."
Jones was arrested on an assault charge in June after being accused of hitting a woman at a nightclub. He has pleaded not guilty and is awaiting trial.
Jones also was arrested in July 2011, when he was accused of being disorderly, shouting profanities and trying to pull away as officers arrested him at a downtown bar.
As part of an agreement to settle that case, Jones pleaded guilty to a misdemeanor count of disorderly conduct and was sentenced to one year of probation and 50 hours of community service.
Last year, Jones was ordered to pay $11 million to two Las Vegas strip club employees injured in 2007 when a gunman claiming he was doing Jones' bidding opened fire outside the club after Jones and his entourage were kicked out. A club manager was paralyzed from the waist down, and a bouncer was wounded.
Jones said he had no role in the shootings and pleaded an equivalent of no contest to misdemeanor conspiracy to commit disorderly conduct. The gunman is serving four to 10 years in prison.
Jones was the sixth overall draft pick in 2005 but repeatedly had off-field issues with his team, the Tennessee Titans, resulting in suspensions. He missed the 2007 season on suspension and sat out the 2009 season when no team was interested in him.
The Bengals gave Jones another chance, and he has taken advantage of it, developing into their third cornerback and punt returner.
Earlier Monday afternoon, before news of Jones' arrest hit, Bengals coach Marvin Lewis and defensive coordinator Mike Zimmer were singing the seven-year veteran's praises. On Sunday, Jones bounced back from an abdominal injury to play in Cincinnati's 34-30 win over the Green Bay Packers. He made four tackles.
"He was sore last week with the abdomen, but he knew it was a big football game, a big opportunity for him and our football team, and he had to play big," Lewis said. "He did a good job."
Zimmer said the performance was among Jones' best since joining the Bengals.
"That may be his best game he's played since he's been here," Zimmer said. "He's played some good games, but that may have been his best one."
Jones, who turns 30 next Monday, may have been celebrating his birthday earlier in the night. At some point Sunday night, he posted a photo from a party to his Instagram and Twitter accounts.
A Sept. 23 story on ESPN.com incorrectly stated that Adam "Pacman" Jones was arrested. He was cited for disorderly conduct. Ohio police officers are directed to issue citations for minor misdemeanors and only to arrest under specific circumstances.
Information from ESPN.com's Coley Harvey and The Associated Press contributed to this report.