The stolen data, the airline said, did not include travel or passport details.
Specifically, the affected period is from 10:58 p.m. BST (2:58 p.m. PT) on August 21 and 9:45 p.m. BST (2:45 p.m. PT) on September 5. It has also said that the breach has now been resolved and customers can book tickets safely.
"We have notified the police and relevant authorities".
Chief executive Alex Cruz says the company is "100% committed" to compensating customers who have had financial information stolen.
"We take the protection of our customers" data very seriously'.
Anyone who believes they may have been affected should contact their banks and credit-card providers. If the organization can not identify the persons affected by the breach, it would make sense that a public announcement of this magnitude to count as notification.
Future bookings will not be affected, BA said.
Mr Cruz said BA had "hundreds" of people communicating with customers "making sure that we can help to protect that data".
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"I've not heard anything from them on this and I've just had to cancel the card I used". But what you do after you call the bank? Probably won't get it back before we fly (ironically).
"Terrible handling of the situation as I've still not received an email from BA!"
The airline also said online check-ins will continue as usual as all systems have resumed functioning normally.
And in May 2017, BA suffered a major computer system failure triggered by a power supply issue near Heathrow which left 75,000 customers stranded. "Every customer affected will be fully reimbursed and we will pay for a credit checking service".
British Airways is the largest airline in the United Kingdom and one of the largest in the world.
This is not the first customer relations problem to affect the airline in recent times.
According to Reuters, the customer data, including personal and financial information involving 3,80,000 transactions, was stolen between August 21 and September 5.