The Gunners ran out 4-2 winners in a memorable meeting at the Emirates Stadium on Sunday, with Metropolitan Police afterwards confirming there were seven arrests made.
It is understood one of those arrests came after a banana skin was hurled from the away end as Pierre-Emerick Aubameyang celebrated scoring an early penalty in front of the Tottenham fans.
“Behaviour such as this is completely unacceptable and the supporter in question will be issued with a ban,” a Tottenham spokesman said.
There were also six arrests for public order offences – at least two of which are believed to be Arsenal supporters who lit smoke canisters during the match.
Aubameyang had opened the scoring before an Eric Dier header and a Harry Kane spot-kick sent Spurs in ahead at half-time.
The Gabon forward went on to equalise, with Arsenal wrapping up the points through Alexandre Lacazette and Lucas Torreira strikes.
Tottenham defender Jan Vertonghen, who had conceded the early penalty for handball, was sent off late on for a second yellow card to round off a forgettable afternoon for Mauricio Pochettino’s side.
The win sees Arsenal move fourth, ahead of Spurs on goal difference, with Unai Emery now focused on another testing examination away at Manchester United in midweek.
“Now I am thinking of the match on Wednesday in Manchester,” he said.
“It is a very big victory, we showed our supporters and we gave them the victory because it is a very special match against Tottenham, for us it is special also.
“But above all it is three points, like against Bournemouth. We are happy, we are enjoying, but shocked because Tottenham are on 30 points like us.”
The unrest was not restricted to the stands as the two sets of players had to be separated following Dier’s equaliser on a feisty afternoon in north London.
The England midfielder celebrated by putting his finger to his lips, with Arsenal substitute Stephan Lichtsteiner reacting angrily to the gesture and referee Mike Dean showing Dier a yellow card.
Pochettino ran down the touchline to help calm matters, with Dier afterwards defending his own actions in the incident.
“I had my back to it all so I’m not too sure what happened,” he said of the scuffle.
“But this is football. It’s a derby. football is all about emotion and I don’t understand how I can get a yellow card in that situation.
“It baffles me because if you take the emotion out of football you’re going to destroy the game for everyone.
“The ref said he gave me the yellow card because it was because of me that the whole thing started.
“If you watch it, we’re celebrating, I don’t leave the pitch at any point and some of their players that are on the bench come to us.
“Their players approached us. I don’t know what’s wrong with it. But it doesn’t matter. It wasn’t because of that we lost.”
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