Hunt will not appeal the suspension, which is without pay.
The former Kansas City Chiefs star was released Nov. 30 after TMZ published a video showing him kicking and pushing a woman. He was also investigated for an incident in June 2017 at a resort in Ohio.
Hunt was placed on the commissioner exempt list the same day he was released by the Chiefs.
"The findings followed a detailed investigation by the NFL, which included reviewing available law enforcement records, video and electronic communications, interviews with numerous witnesses and multiple interviews with Hunt," the NFL said in a news release.
"Hunt has advised the league office that he accepts responsibility for his conduct and the discipline that has been imposed. He has committed to take advantage of available resources to help him grow personally and as a member of the Cleveland community, and to live up to his obligations as an NFL player."
Hunt's suspension takes effect Aug. 31, the date of final roster reductions. He is eligible to play in the Browns' ninth regular season game.
"I want to again apologize for my actions last year," Hunt said in a statement released by the Browns. "I know that my behavior hurt a lot of people, and I again apologize to them. I respect the league's decision on discipline, and I appreciate the time I spent with Commissioner [Roger] Goodell last week."
"I'm grateful for my time with the Browns over the last month and thankful to all the people in the organization that have welcomed me. I also appreciate all of the support I received from my union through this process. My commitment to earning the trust of the league, my teammates, the organization and this community through my actions will continue, and I understand there is a lot of hard work ahead of me before I'm able to fully return to playing the game I love."
Hunt, 23, had 1,202 yards from scrimmage and 14 touchdowns in 11 games in 2018 before his release. The 2017 rushing champion was a third-round pick in the 2017 NFL Draft out of Toledo. Hunt was born west of Cleveland in Willoughby, Ohio.