The 49-year-old, whose career included spells at Newcastle United, Tottenham Hotspur and Rangers, admitted using "threatening or abusive words or behaviour" during his An Evening With Gazza show.
Gascoigne, who lives in Dorset, changed his plea today on what was supposed to be the day of trial.
Dudley Magistrates' Court was told Gascoigne humiliated Errol Rowe, who had been assigned to protect him during his show, by asking him: "Can you smile please, because I can't see you?"
Ordering Gascoigne to pay Mr Rowe £1,000 in compensation, District Judge Graham Wilkinson told the retired star: "You sought to get a laugh from an audience of over 1,000 people because of the colour of Mr Rowe's skin."
The victim was 'shocked' and 'humiliated' at being abused by a 'football icon', the court was told today.
Mr Wilkinson said he applauded the Crown Prosecution Service for bringing the prosecution, and said the victim was humiliated by 'insidious racism'.
See how today's sentencing unfolded
He said the victim was targeted for no other reason than the colour of his skin.
The district judge said the victim was 'clearly humiliated on stage' in front of 'many hundreds of people'.
Mr Wilkinson added: "We live in the 21st century. Grow up with it or keep your mouth closed, Mr Gascoigne."
The judge told Gascoigne - who admitted a racially aggravated public order charge - that his previous convictions were not relevant to the offence.
Mr Wilkinson, who praised the Crown Prosecution Service for taking the case to court, told Gascoigne: "Mr Rowe was clearly humiliated on stage, as part of an act.
"As a society it is important that we challenge racially aggravated behaviour in all its forms.
"It is the creeping 'low-level' racism that society still needs to challenge. A message needs to be sent that in the 21st century society that we live in, such action, such words will not be tolerated.
"It is not acceptable to laugh words like this off as some form of joke."
Gazza entered his plea on the basis that he denied making an earlier comment to Mr Rowe in a dressing room, in which he was alleged to have said: "I didn't know my security had got a sun tan."
Opening the facts of the case, prosecution barrister Simon Davis said Mr Rowe - who has worked for several celebrities - was left shocked and "dazed" at Gascoigne's actions.
Mr Davis told the court: "On November 30 Mr Rowe was employed to provide close protection to Mr Gascoigne at the Civic Hall.
"He would be in a position where he would be putting himself in harm's way should the requirement develop.
"Clearly, there should have been mutual respect between Mr Gascoigne and Mr Rowe."
The court heard Gascoigne - whose show features a question-and-answer session and anecdotes about his career - was addressing the audience when he asked for a tissue and said words to the effect of "I can't tell if he's smiling or not".
According to one witness account, Gascoigne said: "You want to get to the front of the stage and smile so the audience can see you," as Mr Rowe maintained his professionalism in an area of the wings covered by shadow.
Gascoigne was spoken to by police about his comments on December 22 last year.
He told interviewing officers that he "hadn't gone out to offend anybody" but accepted with hindsight that his words had been offensive.
The star, who retired from football in 2005, told police: "Looking back now, obviously I have said the wrong thing. I apologise from the bottom of my heart and it will never happen again."
Defence lawyer Gavin Harris told the court the on-stage comment did not originate from malice, but from Gascoigne's upbringing in "a bygone age" when such comments were commonplace.
Ordering Gascoigne to pay a £100 victim surcharge and a £500 contribution to the cost of the prosecution, the judge hearing the case accepted that the "off-the-cuff" remark was made with little or no thought.
Passing sentence, District Judge Wilkinson told Gascoigne: "You are not a man of huge wealth. You have lived undoubtedly a rollercoaster life.
"I accept that you grew up in a different time. We live in the 21st century. Grow up and live in it or keep your mouth closed Mr Gascoigne."
Gascoigne, who appeared in the dock wearing a pin-striped suit and an open-necked shirt, made no comment to waiting reporters before driven away from court.