A Spurs supporter was arrested after a banana skin was thrown on to the pitch during Sunday's ill-tempered derby with Arsenal at Emirates Stadium.
It was thrown from the away end after Pierre-Emerick Aubameyang had scored for the Gunners, who won the game 4-2.
A Spurs spokesman confirmed the supporter would be banned.
There were also six arrests for public order offences, at least two of which were believed to be Arsenal fans who lit smoke canisters during the match.
"Behaviour such as this is completely unacceptable and the supporter in question will be issued with a ban," a Tottenham spokesman said of the banana-skin incident.
BBC Sport pundit Ian Wright spent seven years at Arsenal, scoring 185 goals in 288 appearances for the club.
"I've played against Spurs and I've taken a lot of abuse but never ever has it been racial," the former striker told Match of the Day 2.
"Now Spurs have to deal with this because some idiot has done that. It's not only embarrassed Spurs but it has embarrassed the Premier League because it has gone around the world.
"It's really unfortunate to see."
There were also unsavoury scenes on the pitch during the match, with the two sets of players had to be separated following Eric Dier's equaliser for Tottenham in the first half.
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Dier celebrated by putting his finger to his lips, but Arsenal substitute Stephan Lichtsteiner reacted angrily to the gesture, prompting a melee.
Tottenham coach Mauricio Pochettino ran down the touchline to help calm matters and Dier said afterwards: "I had my back to it all so I'm not too sure what happened.
"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."
Source: BBC