Tesco Bank became victim to an online hack with customers complaining they had money stolen from their accounts, its chief executive said.
Benny Higgins said some current accounts had money withdrawn from them fraudulently after "online criminal activity" over the weekend.
The bank was earlier forced to block some cards after "suspicious activity" was detected.
Thousands of accounts were reportedly affected, with many people taking to social media to alert the bank to suspicious activity.
Mr Higgins said: "Tesco Bank can confirm that, over the weekend, some of its customer current accounts have been subject to online criminal activity, in some cases resulting in money being withdrawn fraudulently.
"We apologise for the worry and inconvenience that this has caused for customers, and can only stress that we are taking every step to protect our customers' accounts."
He also looked to reassure customers, explaining that Tesco Bank would refund customers "as soon as possible".
One man tweeted his available balance had dropped by £700 without him making a transaction while another said the disruption had left her "unable to feed my kids in school tomorrow".
Others complained about a lack of communication from the bank and hours spent on hold.
"We have been hacked, all money gone, no email or text! Appalling response from Tesco so far #nobodyanswering," one tweeted.
The bank is working with regulators and authorities to look into how the security breach happened.