Maidstone captain George Elokobi jumped into the crowd to confront a Braintree fan at the end of last night's game.
Elokobi, who lives in Braintree and used to play for the Essex club, reacted to a comment from a home supporter behind the goal.
Emotions were running high after Maidstone conceded an injury-time equaliser to draw 1-1.
Several team-mates followed Elokobi into the crowd trying to defuse the situation.
Footage of the incident emerged on social media and the FA look set to get involved.
Maidstone head coach Hakan Hayrettin, a former Braintree manager, said: "George is a local lad, he shouldn't in my opinion react the way he did but obviously words were said to him which he didn't take lightly.
"We'll have to talk to him and see what the club's decision is going forward.
"George played for Braintree, he was a good servant for this club, he came on loan when his career was at a standstill at Colchester and he did ever so well for this club.
"I think maybe a little bit of gratitude, a little bit of humbleness towards him would have been nice.
"I didn't see what happened because I was way back there.
"I got my fair share of stick from the supporters but that's football, you get on with it.
"I believe a few players went into the crowd.
"A few words were said, obviously emotions are running high."
Maidstone chief executive Bill Williams said: "We are investigating the circumstances of an incident after last night's match against Braintree Town.
"The club have been contacted by the Football Association and will respond formally in the coming days."