FA spokesman Andrin Cooper revealed the governing body will be looking into the matter, saying: "This will have nothing to do with the referee's report. He would have been in his dressing room a long way from the incident.
"But we will obviously be asking Chelsea to let us see their CCTV footage of the incident."
Chelsea issued a statement after the game saying they would be "reviewing the relevant footage and will be considering the appropriate course of action".
United have also asked to see the pictures so they can consider what action to take.
The row erupted when the players refused to come off the pitch and an altercation broke out between stewards, groundstaff and the United players.
