Thousands of customers are understood to have been affected, with some saying hundreds of pounds are missing from their accounts.
Tesco Bank has temporarily suspended all online transactions due to a hacking attack affecting thousands of customers.
Some customers tweeted that hundreds of pounds had disappeared from their accounts, with one woman saying the problems meant she would be “unable to feed my kids in school tomorrow”.
Chief executive Benny Higgins confirmed on Monday that some current accounts were subjected to “online criminal activity” at the weekend, with “some cases” resulting in money being withdrawn fraudulently.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 said.
“That is why, as a precautionary measure, we have taken the decision today to temporarily stop online transactions from current accounts.”
He said customers would still be able to use their cards for cash withdrawals and chip and pin payments and that all existing bill payments and direct debits will continue as normal.
Sky News approached Tesco Bank for an interview with Benny Higgins, but this was declined.
However, Mr Higgins told BBC’s Today that about 20,000 customers have had money taken from their accounts, with “suspicious activity” identified in another 20,000 or so.
He sought to reassure customers that Tesco Bank will “ensure they do not lose out financially” and accounts will be refunded “as soon as possible”.
“We continue to work with the authorities and regulators to address the fraud and will keep our customers informed through regular updates on our website, Twitter and direct communication,” he said.
He said the “fraudulent criminal activity” was first identified late on Saturday night.
Many customers posted on the Tesco Bank website and social media saying they were angry with length of time they were kept waiting when they called about their concerns.
“Now on my second attempt at contact by phone, 10 minutes was unacceptable but this time 54 minutes and counting is a serious failure and almost unbelievable,” spidey500 wrote.
“Attempting to log any sort of complaint is virtually impossible despite the platitudes on the main website about making it easy to complain.”
Andyg wrote: “At least you now acknowledge there is a problem.
“I followed your instructions and after 3 hours was able to speak to someone … who wasn’t able to help and just took my name and phone number for someone to call back. No idea when that will be.”
Another customer, Inchindown, wrote: “Because of your failure to be open about this, I have moved all of the money in my tesco current account to another bank. It will remain there until you sort this out.”
Fashion blogger Sam Squire told Sky News: “I was told by text but not until yesterday late afternoon that my account has been frozen.
“They said that they managed to stop the transactions on my accounts so I can’t see any money missing at the moment but they said they can’t guarantee the transactions won’t go through so my account is still frozen and if any transactions go out they will refund the full amount.”
He earlier tweeted: “Love that Tesco Bank haven’t text me until now to let me know there’s been fraud on my account…it’s a bit late now”.
Tesco Bank, which has been wholly owned by Tesco PLC since 2008, has 7.8 million customer accounts.