The last flight out from Entebbe airport to London's Heathrow will depart on 3 October 2015, the UK carrier said.
British Airways operates four flights a week to Entebbe.
In a statement, British Airways said it was "sorry for any disruption" to travellers who had already booked their flights.
Entebbe is Uganda's busiest and only international airport.
Every week, at least 49 domestic flights and 490 international flights depart from there, according to the travel website Tripadvisor.
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