Ian Baldry, 58, made a racist comment towards the City and England winger as he celebrated scoring a goal in a Premier League game against Bournemouth at the Etihad Stadium in December 2018.
The defendant from Yorkshire pleaded guilty in September to causing racially aggravated intentional harassment, alarm or distress.
On Friday, he was sentenced at Manchester Magistrates’ Court and also ordered to complete 200 hours of community service and pay £170 (222 dollars) court costs.
In a witness statement against the defendant another supporter present at the match told police “it was disgusting in this day and age that this was going on.
“I was shocked and offended and felt sick to my stomach when I heard it.”
In another case of racism at a football match England’s Euro 2020 qualifier in Bulgaria was twice stopped due to racism in the stands earlier this season and Gareth Southgate’s team encountered the same issue in another match in Montenegro.
Last season a banana was thrown at Arsenal striker Pierre-Emerick Aubameyang by a Tottenham fan, while Sterling was subjected to alleged racist abuse in a match at Chelsea.
Numerous football fixtures in Italy have also been marred by racism.