The incident took place in last August's Super 8s play-off match against Bradford at Belle Vue Stadium.
Half the fine has been suspended until the end of the season, but Wakefield also have to pay £1,000 for a previous misdemeanour in a game with Castleford.
They got the suspended fine last April after smoke canisters were thrown.
In the match with the Bulls, the Wildcats were found to be in violation of a number of RFL rules with regard to the racist chanting, including responsibility for the behaviour of spectators.
"This was on the basis that the club's immediate response to the incidents did not reach the standards required by the Operational Rules," said a statement by the RFL.
"The tribunal gave credit to Wakefield for the steps taken after the match to address the issue, but felt the sanction should reflect the serious nature of the incidents."
Wakefield Wildcats have been fined £20,000 after being found to be in breach of Rugby Football League rules on racist chanting by fans.