The video, published Monday by TMZ Sports, shows Hunt speaking with multiple officers. Hunt was not arrested and officers did not make a police report about the incident, a police spokesperson told Cleveland.com.
A Browns spokesman said the team is aware of the incident and has spoken to Hunt but had nothing further to say at this point.
The incident took place outside the Barley House in downtown Cleveland. The owner of the bar, Bobby George, told Cleveland.com that Hunt got into a minor altercation with a friend.
Hunt is already suspended for the first eight games of this upcoming season for violating the NFL's personal conduct policy.
The NFL declined comment about Saturday's incident.
Two sources with the Browns told ESPN's Josina Anderson that the team was not concerned at this time, saying based on what they had read, it didn't seem like a big deal, especially because Hunt was not arrested.
Another source characterized the incident to ESPN as "just an argument."
The suspension stems from a February 2018 incident in which he shoved and kicked a woman during an early-morning altercation outside his downtown Cleveland residence, and an incident in June 2018 that involved a physical altercation with other men at Put-in-Bay, Ohio.
Release of the video from the February incident, and the fact that Hunt had lied about it, prompted the Kansas City Chiefs to release him on Nov. 30. The NFL investigated a third incident in Kansas City, but said there would be no discipline stemming from that.
Hunt signed with the Browns on Feb. 11 to a one-year deal worth up to $1.1 million with no money guaranteed.
ESPN's Jake Trotter contributed to this report.