Edward Rabjohn, 21, from Sheffield, made the gesture towards Palmer during the second half of the Sky Bet Championship match between Sheffield Wednesday and the Sky Blues at Hillsborough on January 20.
Rabjohn was caught on camera making the gesture and in a police interview, admitted to the act and to running away from the stadium afterwards.
Palmer reported the gesture to the match referee, Anthony Backhouse, who in turn reported it to Coventry manager Mark Robins.
Rabjohn pleaded guilty to racially abusing Palmer at a hearing at Sheffield Magistrates Court on Monday.
In addition to the banning order, he was sentenced to a two-year community order and 200 hours of unpaid work. The sentence was increased due to the racially aggravated nature of the offence.
Julian Tanikal, District Crown Prosecutor and CPS Yorkshire and Humberside lead sports prosecutor, said: “Racist abuse has no place in society, let alone in sports. While Rabjohn may have quickly realised that he had made an illegal gesture, it should not have entered his mind in the first place.
“Mr Palmer instantly highlighted his abuse, which was then escalated and reported to the police for investigation. I would encourage anyone who witnesses this type of offensive behaviour to report it immediately to help eradicate it from the game.”
