Two of the planes are at London's Heathrow Airport and the third is in Moscow and has not been checked yet, the airline said.
"This is to assess if there is any risk to public health"
British interior ministry
Send us your views
BA said it has been advised that the risk to public health was low.
But it said it was contacting customers who had flown on the planes, which operate within Europe.
In a separate statement, the Britain's interior ministry said that investigators have "started tests on two aircraft at Heathrow Airport [in London] and are making arrangements for a third plane to be tested."
"This is to assess if there is any risk to public health," it said.
Litvinenko, a former Russian spy, died last Thursday of radiation poisoning.
Significant amounts of radioactive Polonium 210 were found in his body.