Macdonald said the bank’s fraud experts were available at all times, including over the public holidays.
ASB Securities is the bank’s share trading platform.
The bank said anyone who clicked on a suspicious link or handed over their payment details should block their cards and contact their bank immediately.
People receiving a suspicious text could report the message to the Department of Internal Affairs for free by forwarding it to 7726.
Macdonald said ASB customers affected could phone the bank by calling 0800 ASB FRAUD (0800 272 372).