In an interview with Hezbollah-owned al-Manar TV on Tuesday, Zasypkin said that "if there is a US missile attack, we - in line with both Putin and Russia's chief of staff's remarks - will shoot down US rockets and even the sources that launched the missiles."
The Russian envoy was referring to comments made by the Russian chief of staff, General Valery Gerasimov, who in March warned that Moscow would shoot down missiles fired towards Syria and would target their launch sites if the attacks threatened members of the Russian army.
Gerasimov said his country would use its weapons against the US if it decided to attack Syrian bases in response to a chemical attack, and if US action endangered Russian army personnel in the country.
In his interview with al-Manar, Zasypkin also said his country made some progress in Syria, including the almost-full "liberation" of Eastern Ghouta near the capital, Damascus, from armed opposition groups.
Zasypkin's remarks come as the US and several European countries threatened to use military action against the Syrian government and its main ally, Russia, in response to a suspected chemical weapons attack on a rebel-held town.
Saturday's attack on the town of Douma in Eastern Ghouta has killed dozens of people, mostly women and children, according to activists and local medics.
The Syrian government and Russia have denied that a chemical attack took place.
On Tuesday, rival draft resolutions by the US and Russia to set up a new expert body to probe chemical weapons attacks in Syria both failed to pass at the United Nations Security Council.
James Mattis, US defence secretary, did not rule out any military action against the forces of Syrian President Bashar al-Assad, while US ambassador to the UN, Nikki Haley, warned Washington was ready to "respond" to the attack regardless of whether the Security Council acted or not.
Meanwhile, the Syrian government has put its forces on "high alert" amid the looming threat of a US military response.
With Russian military assistance, Syrian President Bashar al-Assad launched a bloody offensive on Eastern Ghouta, which had been under rebel control since mid-2013.
Since the start of the aerial bombardment campaign on February 18, the offensive has claimed more than 1,600 civilian lives, and has, through a series of deals reached with rebel groups, internally displaced more than 45,000 people according to the United Nations.