The banana skin has been thrown out of the away end after Pierre-Emerick Aubameyang had shopped for Arsenal.
A Spurs spokesman affirmed the supporter will be prohibited.
There were also six arrests for public order offences, at least 2 of which were believed to be Arsenal fans who lit smoke canisters throughout the game.
“Behaviour such as it is completely unacceptable as well as the supporter in query will probably be issued with a ban,” a Tottenham spokesman said of this banana-skin incident.
There were also unsavoury scenes around the pitch throughout the game, that Arsenal won 4-2, and the 2 sets of players needed to be separated following Eric Dier’s equaliser in the first half.
Dier celebrated by putting his finger on his lips, but Arsenal replacement Stephan Lichtsteiner reacted angrily to the gesture, prompting a melee.
Tottenham coach Mauricio Pochettino hurried down the touchline to help calm issues and Dier said later:”I had my back to it all so I’m not too sure what happened
“But that is soccer. It is a derby. Football is all about emotion and that I don’t know how I can get a yellow card at this circumstance.
“It disturbs me because if you take the emotion out of soccer you are going to ruin the game for everybody.”