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 said the supporter would be banned, with anti-discrimination charity Kick It Out calling for a life ban.
“We condemn this action and welcome the investigation,” Kick It Out said.
Uefa president calls incident ‘a disaster’
Uefa president Aleksander Ceferin said: “We have to do more and campaign more against it, we fine clubs but it is not enough.
“We need to educate the young people but when you see an event like that it is a disaster if you ask me.”
Police said 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.
A Premier League statement said: “Discriminatory behaviour has no place in football or society as a whole.
“The police and the Football Association are rightly investigating and the Premier League will support whatever action they deem necessary.”
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.
“It’s really unfortunate to see.”
There were also unsavoury scenes on the pitch during the match, with the two sets of players having to be separated following Eric Dier’s equaliser for Tottenham in the first half.
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.”