One of Australia's largest banks has apologised to staff who found out they had been fired through an automated email asking them to hand back their laptops.

ANZ's retail banking executive Bruce Rush said it was "not our intention to share such sensitive news with you in this way" as the firm cuts jobs in its retail banking business.

The bank said the emails were sent to some staff ahead of schedule in error. It said it has since stopped sending the emails and that staff have been spoken to personally.

The Financial Sector Union said the email caused "panic and distress" and was a result of the company forcing through a "chaotic pace of change".

The union's president Wendy Streets said it had not been consulted on the changes the bank was making, adding that "ANZ must do better".