Son Heung-min was named as Tottenham's captain for the 2023-24 season
Robert Garland pleaded guilty to racially aggravated harassment in August after shouting and gesturing towards Son in May.
He was initially sentenced to 60 hours of unpaid work and fined £1,384.
However, Spurs and the Metropolitan Police appealed to the UK Football Policing Unit over the sentence.
"The Metropolitan Police, supported by the club, approached the UK Football Policing Unit to seek an appeal against the sentence and, as a direct result, the court issued the supporter with a three-year football banning order," Tottenham said in a statement on Wednesday.
"We thank the police for their cooperation on the matter. We should like to reiterate that the club does not tolerate discrimination of any kind and will always seek for the strongest possible action to be taken against those found responsible."
Garland, 44, made the racial gesture after Son was substituted in the 89th minute during Tottenham's 1-0 home win over Crystal Palace on 6 May 2023.
Son told the police that he did "nothing to be targeted with this horrible racist and discriminatory behaviour", according to the Crown Prosecution Service (CPS).
Kevin Christie from the CPS added: "This case shows that hate crime at football will not be tolerated.
"Garland's actions were rightly condemned on social media and we call on all fans to carry on calling out any form of discriminatory behaviour against players or fans to the police or stewards so we can take cases like this to court."
The Premier League said it "welcomed" the banning order, which means Garland will not be able to go to any regulated match for three years and will need to surrender his passport when international fixtures are scheduled.
"It is vital that those found guilty of discriminatory behaviour are held to account, and this punishment sends a clear message that action will be taken and there are consequences," the Premier League said in a statement on Tuesday.
-- Courtesy of BBC Sport