The airline said it's reaching out directly to customers whose data has been stolen, so keep an eye on your inbox.
According to the company, which disclosed the data theft today, hackers managed to acquire some information about customers who were booking flights on the airline's mobile app and website.
"Please accept our deepest apologies for the worry and inconvenience that this criminal activity has caused".
"We take the protection of our customers" data very seriously'.
BA has notified its customers and advised them to contact their bank or card providers.
It added that no future bookings will be affected.
British Airways informed customers affected by the attack on Thursday, Cruz said.
BA customer Daniel Willis, 34, who booked a flight on Monday with the airline, said he had not been contacted by the airline despite being affected by the data breach.
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"Atrocious that I had to find out about this via news and twitter", he tweeted. But what you do after you call the bank? Typically, we're lucky to get a date range of less than six months to a year, which makes a potential victim's response to any threat hard.
"Terrible handling of the situation as I've still not received an email from BA!"
The hack was not discovered until September 5 and has now been resolved, officials said.
Banks including NatWest and RBS attempted to reassure anxious BA customers that they have "significant" levels of security in place, although they advised account holders to be on the lookout for any suspicious activity.
BA's website has a page with further information on the breach here, where it confirms that "Every customer affected will be fully reimbursed and we will pay for a credit checking service".
British Airways experienced an IT-related crisis in May previous year when roughly 75,000 passengers were stranded after the airline cancelled more than 700 flights over three days because of system problems.
This is not the first customer relations problem to affect the airline in recent times.
Almost 400,000 card payments have been affected (Picture: Getty Images)Which flight bookings were affected by the hack?