NFL Network's Ian Rapoport added the suspension is due to a violation of the league's personal conduct policy.
According to ESPN's Adam Schefter, the suspension stems from a guilty plea to obstruction of official business regarding a January incident.
Mike Garafolo of NFL Network passed along comments from Jones' agent, Peter Schaffer, saying that an appeal was still possible.
Jones was arrested in Cincinnati in January for allegedly making a scene at a bar, pushing a security guard and poking him in the eye and then resisting arrest with the use of physicality, per the Associated Press (h/t CBS News).
According to ESPN.com's Katherine Terrell, Jones pleaded guilty to a misdemeanor after two other charges were dropped in conjunction with a plea deal.
The 33-year-old veteran started 16 games for the Bengals last season and registered 66 tackles, seven passes defended and one interception.
While Jones is out, it is likely that one of Darqueze Dennard, William Jackson III or Josh Shaw will start in his place across from Dre Kirkpatrick.