British Airways contacted affected customers as soon as it found out data from its website and mobile app had been breached, its boss said on Friday.
BA, part of the International Airlines Group, said late on Thursday financial data had been stolen from potentially hundreds of thousands of its customers who made online bookings in recent weeks.
"The moment we found out that actual customer data had been compromised that's when we began an all-out immediate communication to our customers, that was the priority," Alex Cruz, BA's chief executive and chairman, told BBC radio.
He said any customers who lose out financially will be compensated by the airline.
Cruz said the hack was not a breach of the airline's encryption.
"No, our data is encrypted," he said. "There were other methods, very sophisticated efforts, by criminals in obtaining the data," he said.
"It was having access to our systems in an illicit way, it was very sophisticated."