The Foreign Secretary also said the country has a duty to ensure England fans travelling to football’s biggest tournament this summer are protected.
In response to Mr Johnson’s claims, a spokeswoman for the Russian foreign ministry said he was “poisoned with hatred and anger”.
The row came after Russia accused Britain of deliberately concealing evidence in the escalating war of words over the Salisbury nerve agent attack.
While the Foreign Office has so far stopped short of advising fans not to go to the World Cup, starting in June, Mr Johnson said they were monitoring the situation “very, very closely”.
Giving evidence to the Commons Foreign Affairs Committee today, he was challenged by Labour MP Ian Austin as to whether he thought Vladimir Putin intended to use the World Cup “in the way Hitler used the 1936 Olympics” as a propaganda exercise to “gloss over” Russia’s “gross human rights abuses”.
The Foreign Secretary replied: “I think that your characterisation of what is going to happen in Moscow, the World Cup, in all the venues - yes, I think the comparison with 1936 is certainly right.
“I think it’s an emetic prospect, frankly, to think of Putin glorying in this sporting event.”
During the 1936 games, Adolf Hitler – while attempting to flaunt his dominance on the world stage – was incensed as African-American sprinter and long jumper Jesse Owens won four gold medals.
In a further development to the nerve agent row yesterday, Russia’s foreign ministry head of non-proliferation and arms control insisted Moscow bore no responsibility for the incident and dismissed British demands for an explanation as “absurd”.
At a “briefing” for foreign diplomats in Moscow, Vladimir Yermakov questioned whether the incident, which left former Russian double agent Sergei Skripal and his daughter, Yulia, fighting for their lives even involved a nerve agent.
“All the facts are being concealed intentionally and the real evidence could (have) vanished. This has happened before in Great Britain, repeatedly,” he said.
However, while giving evidence to MPs, Mr Johnson said the trail of evidence led to the regime of Russian President Vladimir Putin.
Mr Johnson said: “As we saw in the case of the murder of Alexander Litvinenko, the trail of responsibility for such assassinations and assassination attempts does lead inexorably back to the Kremlin.”
Britain expelled 23 Russian diplomats after military scientists at Porton Down concluded the Skripals had been poisoned by a Russian-made Novichok nerve agent and the Kremlin then failed to respond to Theresa May’s demand for an explanation.
The Russians in turn announced the expulsion of 23 British diplomats as well as the closure of the British Council and the British consulate in St Petersburg.
Mr Yermakov complained that the Russians had been denied consular access to Ms Skripal, who remains a Russian citizen, and said that it was up to the UK authorities to explain what had happened.
“This took place on the territory of Great Britain,” he said.
The Skripals tonight remained in hospital after falling critically ill in the Wiltshire city on March 4.