A Tottenham 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 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.
“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 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.
“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.
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.”