British Airways said in a statement it was notifying customers on cancelled services and would offer full refunds.
Russia has banned all United Kingdom registered airlines from landing at its airports or crossing its airspace.
The Russian civil aviation regulator said on Friday.
The move followed UK’s ban on the flights of Russian flag carrier, Aeroflot in response to Russia's invasion of Ukraine.
Virgin Atlantic and British Airways are the airlines that are most affected by the Russian decision, last night both airlines already used a southern route en route to London Heathrow where normally the airlines would use Russian (and Ukrainian) airspace.
Russia's civil aviation authority said: "This measure was taken in accordance with the provisions of the Intergovernmental Air Services Agreement between Russia and the UK as a response to unfriendly decisions by the UK aviation authorities regarding the restriction on regular flights of aircraft owned, leased or operated by a person associated with Russia or registered in Russia."
British Airways said in a statement it was notifying customers on cancelled services and would offer full refunds.
"We apologise for the inconvenience but this is clearly a matter beyond our control," the airline said.
"We will continue to monitor the situation closely."
British Airways normally operates three flights per week each way between London and Moscow.