Dynamo fans raised a banner dedicated to Adolf Hitler's deputy Rudolf Hess during the game against Vitebsk on April 28.
"It has brought shame not only to Belarus football but to the entire nation," the country's FA disciplinary chief Vladimir Vitushko told reporters after slapping Dynamo with a 245 million roubles ($82,000) fine, the biggest in Belarus football.
Vitushko said he did not know who was behind the action.
Dynamo, the country's most popular club with seven league titles who finished second last year, said they would appeal.
The banner read: "Your life is an example of loyalty for us", and had a portrait of Hess on it with his date of birth and death. It was intended to celebrate the 116th birthday of Hess, who died in prison in west Berlin aged 93 in 1987.
The fans' action has outraged many people in the former Soviet republic, coming just days before the country is due commemorate the 65th anniversary of the Nazi Germany's defeat in World War Two.
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