Clubb was charged by the Rugby Football League's match review panel with a Grade F offence after Hull FC's Andre Savelio made a formal complaint following last Thursday's Betfred Super League match.
The 33-year-old was suspended by his club a day later as they launched a joint investigation with Hull and on Tuesday he appeared in front of an independent operational rules tribunal which found him guilty.
The ban is the minimum normally applied for Grade F offences and included mitigating circumstances after the tribunal considered submissions from both players and clubs as well as character references and broadcast footage.
His Honour Judge Guy Kearl QC, who chaired the hearing, said: "We have considered the evidence of both players and the circumstances surrounding the allegation and find that we are reasonably satisfied, taking into account the seriousness of the charge, that the words were said, albeit in the heat of the moment, but nevertheless were said.
"They do constitute unacceptable language based on (a player's) racial and ethnic origin and therefore we find that this was serious misconduct which has brought the game into disrepute.
"On the other hand we have considered the character references placed before us by Wigan Warriors from those who know (Tony Clubb) well at the club.
"We do not find that he is a racist, simply that on this occasion he used unacceptable language in the heat of the moment.
"We have therefore reduced the penalty to take account of his character and good disciplinary record to a suspension for eight matches and a £500 fine."
Savelio, who was born in New Zealand and has Samoan heritage, spoke out in the wake of the allegations, saying he would not "sit quietly" and said he had intended to deal with the issue himself during the game but, after Clubb was taken off the field and did not return, he reported it to referee James Child.
The suspension starts on Saturday, when Wigan and Hull meet again, this time in the Challenge Cup, and Clubb will be free to play again in July but he could be facing an uncertain future.
He turns 34 in June and is out of contract at the end of the season.
Clubb has made 157 appearances for the Warriors since joining them from the Broncos in 2014 and was in their Grand Final-winning team of 2018.
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