BA launched a programme to boost morale among cabin crew by encouraging them to mix more.
But the initiative - dubbed 'Hug A Pilot' - was taken to extremes by the married man and the stewardess on a foreign stopover between flights.
The pilot's wife is also believed to be a British Airways employee but is apparently standing by him, The Sun reported.
The stewardess, based at Heathrow's Terminal 5, has now been moved to a regional engineering base. She is planning to keep the baby.
When the pilot, who earns £100,000 per year, discovered that the young employee was pregnant he apparently denied it was anything to do with him but later confessed.
A spokesman for British Airways declined to comment.
The pilot and his wife are also apparently based at Terminal 5.
A source at the airline told The Sun: 'The girl's pregnancy and move to engineering is the talk of the airline. She was stunned to find she was expecting, but wants to keep the baby.
She will be looked after financially because of the captain's pay.
he airline employee 3,000 pilots and 13,500 cabin crew.
As part of the 'Hug A Pilot' scheme, all staff are being urged to mix more to boost morale.
BA’s mandatory Safety and Emergency Procedures three-day training session for staff now has a new 90-minute team work discussion.
One crew member posted on an internet forum: 'It transpires at SEP on the first day, BA have now introduced how to interact and socialise with the "pilot community".
The session includes pre, during and post flight interaction, you will now be advised it’s inappropriate and bad mannered not to include everyone on the crew and pilots while socialising in the bar or down route.'
Following the pregnancy the source, speaking to The Sun, added: 'The Hug A Pilot edict was not supposed to lead to this.