Jones' suspension stems from his January arrest at a hotel in downtown Cincinnati, where he allegedly pushed a security guard, poked him in the eye and refused to comply with law enforcement officers.
Jones had faced misdemeanor charges of assault, disorderly conduct and obstructing official business and a felony count of harassment with a bodily substance for allegedly spitting on a nurse in jail, but most of the charges were dropped at the request of a Cincinnati prosecutor, who said the incident was just "drunken foolishness."
Jones pleaded guilty in May to the obstruction charge. He was sentenced to two days in jail, which had already been served.
The NFL told Jones in a letter that it watched video "of the tone, tenor and nature of your interactions with law enforcement at the site of your arrest, during transportation to the jail, and during the booking process." The league also said his actions reflected poorly on him, his family, the Bengals and the NFL.
"While it is our understanding that appropriate apologies have been publicly extended, they do not completely negate your behavior and admission of culpability for the underlying conduct," the NFL wrote.
In a statement, the Bengals said they had anticipated the suspension and were looking to move on.
"Our focus is on getting ready for the upcoming season," the Bengals said. "Adam will participate in training camp, and we are counting on him to help our team when he returns from suspension."
The Bengals host the Baltimore Ravens in Week 1. Jones would be allowed on Cincinnati's active roster the day after the game. He will be allowed to participate in preseason practices and games.
Jones has three days to appeal the suspension. His agent, Peter Schaffer, said they are reviewing all options in regard to a potential appeal.
Jones' participation in preseason games would be departure for the Bengals from last season, when linebacker Vontaze Burfict did not play in the preseason ahead of his three-game suspension to start the regular season.
In a video released by Cincinnati police, Jones was shown cursing at an officer in the back of a police car and telling him, "I hope you die tomorrow." Jones apologized in court for the incident.
Jones said he has been going to anger management classes and alcohol-related treatment since the arrest. He made headlines in April for yelling at a local reporter who asked questions about the arrest.
The 33-year-old has a history of off-the-field incidents, including one that almost ended his career. He was suspended without pay by the league for the 2007 season after an incident in a Las Vegas nightclub resulted in a man being paralyzed. Jones was later ordered to pay $12 million in damages to the victim.
Jones has been with the Bengals since 2010 and was voted a team captain for the first time in 2016. Bengals owner Mike Brown publicly stood by him after the arrest.
"He knows full well what he has done to himself," Brown had told Bengals.com and the Cincinnati Enquirer as part of his statement. "He regrets it. But it's been made into a public issue, and maybe I am overly tolerant. If so, so be it."