ANZ customers received a notice from the bank explaining that changes were being made to the site.
However, the notice said the changes are cosmetic and services will not be affected.
Craig Reardon, director of e-commerce consultancy business The E Team made a complaint to ANZ at the start of the week requesting access to his online accounts. He says he is still awaiting a response.
Reardon, who holds three personal and two business accounts with ANZ, said all accounts have been affected.
He said most of the problems come after logging-in, when the service grinds to a halt.
"Basically all this week, I have attempted to use the public site and my online banking accounts and cannot even get access," Reardon said.
"There is a notice on the site saying it is making changes and only appearance and functionality will be affected, not performance.
"To indicate how bad it is, I haven't been able to log in to do online banking at all today, which is a major inconvenience for a business that does everything online."
A spokesperson for ANZ Bank confirmed Internet banking customers have been "experiencing difficulties" and the bank is currently looking into the cause.
"We are investigating the cause of this and are working to resolve the matter as quickly as possible," the spokesperson said.
"We would like to apologize to customers for any inconvenience and assure them that we are dealing with this as a priority."