Tesco Bank has halted online payments for current account customers after money was taken from 20,000 accounts.
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.
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the bank confirmed some accounts "have been subject to online criminal activity, in some cases resulting in money being withdrawn fraudulently".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.
It is not clear as to the true scale or cause of this issue. However, it does rather call into the question the security of banking online and the desire by some in banking and politics to rush us towards a cashless society!