A man has been charged after a banana skin was thrown onto the pitch during Sunday's ill-tempered derby with Arsenal at Emirates Stadium.
Three other men have also been charged following incidents at the match.
The banana skin was thrown from the away end when Pierre-Emerick Aubameyang scored for the Gunners, who won 4-2.
A Spurs spokesman said the fan who threw it 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.
"Our latest reporting figures show incidents of racism are on the rise and the banana throwing at the north London derby should be seen in that context."
Police say three men have been bailed to appear at Highbury Corner Court on Tuesday, 18 December, while the other has been bailed to attend the same court on Monday, 31 December.
Six arrests were made in relation to the match, with two other men released with no further action.
Uefa president calls incident 'a disaster'
"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.
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."
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.
"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 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."