Alexander Yakovenko said “nobody had the right” to compare Russia – which lost 25 million lives in World War Two – to Nazi Germany.
He said it was an insult to British war veterans from the Arctic convoys.
Russia says the UK had “no proof” it carried out the attack in Salisbury.
Prime Minister Theresa May has said the chemical used in the attack had been identified as being part of a group of nerve agents developed by Russia, known as Novichok.
She will later tell an EU summit the poisoning of Sergei Skripal and his daughter Yulia shows Moscow has no respect for international law.
The pair remain in a critical condition in hospital after they were found unconscious on a bench on 4 March.
Mr Johnson made the comment at a Foreign Affairs Select Committee meeting on Wednesday.
The foreign secretary agreed with the comparison made by Labour MP Ian Austin, adding: “Your characterisation of what is going to happen in Moscow in the World Cup, in all the venues, yes, I think the comparison with 1936 is certainly right.
“I think it is an emetic prospect frankly to think of [Russian President Vladimir] Putin glorying in this sporting event.”
‘Beyond common sense’
Speaking at the Russian Embassy in London, Mr Yakovenko said Moscow considered the foreign secretary’s comments “unacceptable and totally irresponsible”.
“The British government is free to make a decision about its participation in the World Cup,” he said.
“But nobody has the right to insult the Russian people – who defeated Nazism and lost most than 25 million people – by comparing our country to Nazi Germany.
“That goes beyond common sense. And we do not think British war veterans – including those of the Arctic convoys [which shipped four million tonnes of armaments and essential supplies to the Soviet Union during World War Two] – would share this opinion.”
‘Refuses to cooperate’
Mr Yakovenko’s response came as he gave a statement on Russia’s latest position regarding the Salisbury attack.
He criticised the British government for refusing to share information and provide the Russian government with a sample of the nerve agent.
He said Mrs May had “built the official position on assumptions”, adding: “Britain has, without any evidence, blamed Russia of poisoning of three people [the Skripals and Det Sgt Nick Bailey who was part of the initial response to the incident] and continues to refuse to cooperate.
“We cannot accept that.”
But Mrs May will stick with her conclusion and tell EU heads of state that although the attempted assassination of the Skripals took place on UK soil, the Russian threat does not respect borders and places all European nations at risk.