REUTERS/Toby Melville
The airline had been flying four times per week to the two countries, traveling first to Freetown before continuing on to Monrovia.
The World Health Organization says more than 800 people in Guinea, Sierra Leone, and Liberia have died in the outbreak. There is no known treatment for Ebola.
BA says customers with tickets on those routes are being offered refunds or the ability to rebook flights for a later date.
"The safety of our customers, crew and ground teams is always our top priority and we will keep the route under constant review in the coming weeks," BA said.