The Blades said they were aware of the footage which has been circulated on Twitter and claims to involve the player signed from Swansea City in 2019.
Bramall Lane officials are now looking into the events surrounding the 25-second clip which includes several people and also appears to show a scuffle and the recording device being stamped on after it is dropped.
A club spokesperson said: “Officials at Sheffield United are aware of the video circulating on social media and are currently investigating.”
Scotland international McBurnie has made 65 appearances in all competitions this season but is currently out injured. The foot injury sustained last month means the 24-year-old is almost certain to miss this summer’s European Championships after helping Steve Clarke’s side qualify for the tournament for the first time since 1996, appearing in both play-off wins over Israel and Serbia.