The video, which emerged on social media over the weekend, appears to show Mr McBurnie in an altercation with a number of young men on Knaresborough High Street.
The man in the video stamps on the phone the footage is being recorded on, before appearing to fight with another man.
North Yorkshire Police has confirmed a 24-year-old man has been arrested following an incident in Knaresborough on Saturday.
A statement reads: "A 24-year-old man from Knaresborough has been arrested in connection with an incident, which involved another man being assaulted.
"The 24 year old arrested man remains in custody at this time."
The 21 year old victim sustained facial injuries during the incident, which happened shortly before 8.30pm on Saturday, May 8 on High Street in Knaresborough.
Anyone who witnessed the incident is asked to contact police by dialling 101, choosing option 1 and passing information to the force control room, quoting reference number: 12210115038.