The incident occurred when fans invaded the pitch at the City Ground after Forest had beaten the Blades on penalties in the second leg of Tuesday night’s Championship play-off semi-final.
A video circulating on social media shows McBurnie, sidelined through injury, tangling with a supporter who had fallen to the ground. Forest fans had poured on to the pitch in celebration after their side’s penalty shootout win secured their place in the play-off final at Wembley.
The FA has confirmed that it was aware of the footage and was looking into it.
Nottinghamshire Police confirmed that a 25-year-old man presented himself to police and was arrested on suspicion of assault, before being released on police bail.
Detective Inspector Nicholas Hall, of Nottinghamshire Police, said: "We are working hard to understand the sequence of events depicted in this video and have now interviewed a suspect.
"As our investigation continues we would like to speak to any other witnesses who have not yet come forward."
On Wednesday night, McBurnie responded to a message on Twitter, posted by a Blades fan, which said: “Wish that video was in full context – looks more like he was trying to step over him with one bad leg! Could be wrong!”
McBurnie endorsed the tweet with a “100” emoji – taken to mean he agreed 100 per cent – but said nothing else.
He also ‘liked’ a tweet posted by Blades’ assistant kit man Adam Geelan, which said: “Fan illegally enters the pitch provokes and tries to push Rhian (Brewster) he defends himself and the kid falls on Oli’s broken foot can clearly see there’s no stamp, ridiculous post especially when stewards and police were stood there watching it happen and was left to ourselves to defend.”
In a separate incident at the City Ground, a 30-year-old man was jailed for headbutting Sheffield United captain Billy Sharp at Tuesday’s play-off semi-final at Nottingham Forest’s City Ground.
Forest season ticket holder Robert Biggs, from Ilkeston, Derbyshire, admitted assault occasioning actual bodily harm which left Sharp requiring four stitches to a wound to his lip. He was jailed at Nottingham Magistrates’ Court on Thursday for 24 weeks.