The 24 second mobile phone clip, filmed in Knaresborough, North Yorkshire, is reported to show Blades striker McBurnie in a brawl with 21-year-old insurance broker Elliott Wright.
A man is seen stamping on a mobile phone, which was dropped to the ground during the incident but continued to capture scenes and audio.
The clip has been seen more than half a million times on social media.
Sheffield United confirmed yesterday that the club was aware of the video and said today that the police were involved.
In a statement, the club said: “Officials at Sheffield United are aware that police are now involved following the emergence of a video circulating on social media over the weekend and as a club we will do all we can to assist enquiries, as well as continue our own investigation.”
McBurnie, a Scottish international, signed for Sheffield United from Swansea for £20 million when the Blades were promoted to the Premier League.
The £20,000 a week forward is currently out injured after suffering a stress fracture in United’s 3-0 defeat to Arsenal last month.
North Yorkshire Police said: “A 24-year-old man from Knaresborough has been arrested in connection with an incident which involved another man being assaulted.
“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.
“The 24-year-old arrested man remains in custody at this time.”