None of the United players who played in the match were involved but players Patrice Evra, Gary Neville, Paul Scholes, Gerard Pique and John O'Shea were all warming down when an argument began with the ground staff tending the pitch.
Stewards quickly moved in to separate those involved but after the situation quietened down the row flared up again, although no punches were thrown.
The incident came a few minutes after Chelsea beat Manchester United 2-1 to pull level with United at the top of the table.