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 Sky Bet 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 confirmed that it was aware of the footage and was looking into it, while Nottinghamshire Police said they were also investigating.
Inspector Andy Wright said: ‘We have been made aware of a video circulating on social media showing a possible altercation where a Forest fan can be seen on the ground following the play-off semi-final.
‘We have now started an investigation into this incident. The person in question has not yet reported the incident, but we would urge them to come forward along with any other persons who may have witnessed the incident or have video footage so we can establish the full circumstances.
‘We would particularly appeal to the owner of the original footage to make contact.’
Neither Sheffield United or Forest have commented on the incident.
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 Rian (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.’
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