Appearing at Dudley Magistrates' Court, Gascoigne admitted a racially aggravated public order offence, using "threatening or abusive words or behaviour", on November 30 during his show An Evening With Gazza in Wolverhampton.
Gascoigne made a 'joke' about a black security guard during his performance in Wolverhampton, the court heard.
The Judge said by pleading guilty, Gascoigne accepted that he "singled out" victim Errol Rowe because of the colour of his skin.
He was fined £1,000 and ordered to pay £1,000 to the victim and pay £500 costs.
Sentencing, District Judge Graham Wilkinson said: "It is the creeping low level racism that society must challenge.
"I accept you grew up in a different time, but we live in the 21st century. Grow up with it or keep your mouth shut, Mr Gascoigne."
ITV News correspondent Ben Chapman was at Dudley Magistrates' Court:
The court was told Gascoigne "humiliated" Mr Rowe by asking in front of more than 1,000 people: "Can you smile so that I can see you?"
An audience member said that the footballer "clearly thought what he said deserved a laugh" and some of the audience did laugh.
Mr Rowe said that Gascoigne was his "hero" and the incident has led him to have flashbacks of being racially abused in front of a large crowd.
Through his lawyer, Gascoigne denied he was a racist and apologised to the victim and never intended to offend anybody.
On the way into court, Gascoigne signed autographs and took selfies with fans waiting outside.
Gascoigne, 49, known as "Gazza", was described as the most gifted footballer of his generation at his peak in the 1990s, playing for Spurs, Newcastle Utd, Everton and Glasgow Rangers.
But he has suffered recurring bouts of alcoholism and drying out before relapsing.