Hunt, who led the NFL in rushing in 2017, was let go by the Chiefs after a video surfaced that showed him shoving and kicking a woman during an altercation at a Cleveland hotel last February.
Hunt was placed on the Reserve/Commissioner Exempt List and cannot play as long as he is on that list. The NFL is investigating the February incident as well as a June incident in which he allegedly punched a man at an Ohio resort.
No team claimed Hunt and the rest of his rookie contract, which means any team can negotiate with Hunt and sign him.
If he signs with a team, Hunt probably faces a suspension of at least six games for violating the league's personal-conduct policy.
On Monday, Chiefs head coach Andy Reid discussed why the team decided to cut Hunt.
"I don't think anybody necessarily wins in this situation," Reid said, according to the Kansas City Star. "I'm hoping and would like Kareem to get help along, obviously, with everybody that was involved with it. It's a tough deal. It's not a win-win situation for anybody, the young lady included.
"My prayers are that everybody involved gets help. Most of all, we're all in this fraternity of this earth life and we're all living together. ... My primary objective always is to try to make sure everybody ends up a better person and we can all live together with some kind of continuity and peace."
Hunt apologized for his actions during an interview with ESPN on Sunday. He also said the Chiefs did the right thing in releasing him and admitted he did not tell the truth to team officials when he gave his initial account of the February incident.
"The Chiefs are right. I didn't tell them everything and I don't blame them for anything," Hunt said in the interview. "My actions caused this. I really wish I could just apologize to them and let them know it's no hard feelings between me and the Chiefs. I love the program. I love the people there. I just want to take this time and better myself and not let anything like this ever happen again."