The airline informed travel companies on Tuesday that: "British Airways services from London Heathrow to Freetown and Monrovia will be temporarily suspended from tomorrow, 6 August until 31 August 2014, due to the deteriorating public health situation in both countries."
Liberia and Sierra Leone are among four West African countries affected by the deadly outbreak of the Ebola virus.
British Airways is offering affected customers the option of a full refund or rebooking.
As of August 1, the World Health Organization had recorded 1,603 cases of confirmed, probable and suspected Ebola, including 887 deaths.
The Ebola virus is spread by close contact and typically kills up to 90 percent of its victims. There is no known cure or antivirus.