The airline said it regularly evaluated its routes "based on where customers tell us they want to travel".
Campaigners opposed to the airport's expansion plans said the announcement showed "the world has changed" as a result of the coronavirus crisis.
A spokesman for Leeds Bradford Airport said they were "disappointed" by the decision and hoped BA would return in the future.
The decision comes after it was reported BA would be cutting up to 12,000 jobs because of a collapse in business brought on by the coronavirus pandemic.
The 10 flights a week connecting Leeds Bradford Airport and London Heathrow will now stop.
In a statement, BA said: "We are sorry to suspend our flights to Leeds Bradford after many years.
"We regularly evaluate our routes based on where our customers tell us they want to travel."
BA is in contact with customers to provide them with alternative options.
The spokesman for Leeds Bradford Airport said: "Domestic and international connectivity remains critical to support business and the region's economy and we hope to welcome BA back in the future."
The BA announcement comes as campaigners said posters opposing the airport's planned expansion had gone up around the city.
The Group for Action on Leeds Bradford Airport said it showed "the claims... about job creation are simply not credible".
However, the airport said BA accounted for "a fractional percentage of our passenger numbers".
It added that expansion would create "thousands of highly skilled, permanent positions, as well as hundreds of construction jobs".
BA has said it expects it will take several years for air travel to return to pre-coronavirus levels, a warning that has been echoed by airlines worldwide.
British Airways has axed flights to Leeds Bradford Airport.