No flights after August 16
OpenSkies, BA's all business class airline, is to suspend flights from Amsterdam to New York from August 16.
The daily service began last October.
The BA subsidiary said it would now "re-focus" on its remaining route, Paris-New York.
Dale Moss, OpenSkies' managing director, said: "The economic environment has produced a significant drop in market demand.
"While OpenSkies developed more than 16% market share during only nine months, it was not enough to sustain a profitable service at this time.
"Moreover with remaining uncertainty over the near term, suspending the service clearly was the most prudent decision to preserve our resources."
OpenSkies started operations in June 8, 2008 with the Paris-New York service.
A month later it bought L'Avion, a French all business class airline operating the same route.
BA declined to deny a report last week that it was planning to sell OpenSkies.
Reuters said that Reynolds Partners, a London-based independent investment bank, had been asked to find a buyer for the airline.
The report came a week after Mr Moss, said the carrier had missed its first year financial targets.
Mr Moss, speaking at the Business Travel Market in London in June, said it would "persevere" despite a drop on around 45% in business traffic on its two routes Paris and Amsterdam to New York.
Reuters reported that BA wanted to sell a majority stake in OpenSkies, preferably in the next two or three months.
BA said in a statement it said: "We are reviewing all aspects of our business in the current economic environment.
"OpenSkies is a small part of our business and its losses are not significant compared to losses in other parts of the company."
It is going ahead with plans to launch an all-business class service form London City Airport to New York on September 29
BA announced on July 17 that it had completed the terms of its plan to raise £350m through a convertible bonds issue.
The airline which is aiming to raise about £600m cash, said it had also agreed terms with the trustees of its pension scheme to raise up to £330m through releasing some bank guarantees.
BA's Willie Walsh has said the carrier is in a battle for survival.