Kelly Gregory made the remarks about a black player while Mansfield Town were 4 -1 down to Crewe Alexandra, on July 4.
Prosecutor Robert Carr said: “A number of members of the crowd were expressing their anger at the time.
“A witness said that she came out with a comment that overstepped the mark. She continued to be abusive. Children were coming through for the half-time interval.”
When the witness, who had his 14-year-old son with him, told her to shut her mouth, Gregory shouted: “I will come and smack you in the mouth.”
Stewards escorted her to the ticket office and the police were involved.
Mary Dixon, mitigating, said: “Obviously, feelings were running high. She admits that these remarks are unacceptable in this day and age.
“Going to football is one of her only pleasures. She had been wound up by the performance of the Mansfied Town players.”
Mrs Dixon urged the judge not to impose a banning order, as it was “an inflammatory remark made in the spirit of the moment.”
Gregory, 38, of Winkburn Road, admitted two counts of using threatening words, one of which was racially aggravated, when she appeared at Mansfield Magistrates Court, on Wednesday.
District judge Jonathan Taaffe said: “This was vile racist abuse you made while Mansfield were losing heavily at the time. But that’s no reason to vilify or abuse someone because of the colour of their skin.”
She was fined a total of £200, and ordered to pay £85 costs and a £30 government surcharge. She was banned from attending Mansfield Town matches for three years.