When handing down the sentence, the judge told Cheryl: "You showed no remorse whatsoever."
But he said he didn't think Cheryl would get in trouble again.
The 20-year-old of Heaton, Newcastle, gasped when the guilty verdict was announced at Kingston Crown Court in Surrey.
Her solicitor read a statement from Cheryl as she left the court.
"I am thankful that the jury have accepted that this incident had nothing to do with race.
"I am not a racist and anyone who knows me knows that I wouldn't say anything racist."
Cheryl said she was "stunned and disappointed" by her conviction.
The trial opened on Thursday, 9 October.
The court was told that a row had broken out between Cheryl and Sophie about payment for some lollipops at The Drink nightclub in Guildford.
Cheryl told the court that she had hit Sophie, but it was in self defence.
The incident took place when the singer visited the club with bandmate Nicola Roberts in January.
Cheryl had denied assault and racially-aggravated assault.