Tesco Bank has halted online payments for current account customers after money was taken from 20,000 accounts.
The bank's chief executive Benny Higgins told the BBC he was "very hopeful" customers would be refunded within 24 hours.
About 40,000 accounts saw suspicious transactions over the weekend, of which half had money taken, he said.
Customers will still be able to use their cards for cash withdrawals, chip and pin payments, and bill payments.
They can also use online banking, but cannot make online transactions until the situation is back under control, Mr Higgins told the BBC's Today programme.
Earlier, the bank confirmed some accounts "have been subject to online criminal activity, in some cases resulting in money being withdrawn fraudulently".
Mr Higgins also apologised for the "worry and inconvenience" that customers have faced.