The carrier normally operates a four-times-a-week service from Heathrow to Freetown in Sierra Leone, with a connection on to Monrovia in Liberia.
BA said: "We have temporarily suspended our flights to and from Liberia and Sierra Leone until August 31 due to the deteriorating public health situation in both countries.
"The safety of our customers, crew and ground teams is always our top priority and we will keep the routes under constant review in the coming weeks.
"Customers with tickets on those routes are being offered a range of options, including a full refund and the ability to rebook their flights to a later date."
It came as health officials said they had been made aware of a Welsh person believed to have come into contact with the deadly Ebola virus.
The person visited West Africa where more than 1,600 people have been infected with the virus in recent months, resulting in 887 deaths.
Public Health Wales said the person is "currently staying away from work and limiting contact with other people voluntarily".
A statement from the authority said: "The individual does not have symptoms of Ebola and there are no cases of Ebola in Wales."
Ebola is one of the world's deadliest diseases, with up to 90 per cent of cases resulting in death.
The incubation period, the time between infection and the onset of symptoms, ranges from two days to three weeks. No vaccine or cure is available.
The symptoms of Ebola are severe, with patients often overcome by a sudden onset of fever as well as weakness, muscle pain and headaches.