In 1962, Soviet-US relations were tested to the limit when America discovered the Soviet Union planned to deploy nuclear missiles in Cuba.
Now the US wants to build a defence shield in Poland and the Czech Republic, both former Soviet states, saying it needs to defend itself aganst Iran and North Korea.
Putin sad: "For us, technologically, the situation is very similar. On our borders such threats to our country are being created."
Russia says the shield will threaten its security and lead to an arms race.
Putin has offered the US the chance to use a radar station in Azarbaijahn instead.
In Washington, Sean McCormack, the state department spokesman, strongly rejected Putin's comparison between the US missile shield proposal and the Cuban crisis.
He said: "There are some very clear historical differences between our plans to deploy a defensive missile system designed to protect against launch of missiles from rogue states such as Iran, and the offensive nuclear capability of the missiles that were being installed in Cuba back in the 1960s.
"They are not historically analogous in any way, shape or form."