"I want to apologize for my actions," Hunt said in a statement to ESPN. "I deeply regret what I did. I hope to move on from this."
The video of Hunt, published by TMZ Sports, is related to an incident in February at a downtown Cleveland hotel where the running back has an apartment, the Star reported.
Police were called and a written report was made, but Friday was the first time video footage of the incident had been available, the newspaper reported.
In an email to the Star, NFL spokesman Brian McCarthy said, "Neither the NFL nor the Chiefs viewed the video before it became public today."
Hunt had rushed for 824 yards and seven touchdowns for the Chiefs (9-3) who own the best record in the AFC this season. For his career, Hunt has rushed for 2,151 yards and has scored 15 touchdowns.