The bank has stopped online applications for new home loans as it struggles to deal with demand.
The big four lender told Newshub that it had to "temporarily pause online applications for new home loans", but gave no indication of when they would return.
ANZ's decision is the latest clear sign that banks are struggling to deal with turnaround times, with processing taking longer than ever for home loan customers.
Newshub also reported that Kiwibank customers had faced a significant delay in getting loans approved ahead of March's new LVR restrictions.
Banks have struggled for years with turnaround times, but Covid-19 mortgage deferrals have added to the backlog of under-staffed banks.
ANZ redeployed staff into its home loan business last year, but advisers report no real improvement in the bank's processing times.
Turnaround times continue to be the main headache for advisers and their clients. In the latest edition of TMM, top advisers said they expect processing backlogs to be their biggest issue in 2021.
While customers rush to get ahead of the March LVR deadlines, many banks have enforced the rules already.
Owner-occupiers will need a 20% deposit in most cases, while investors will need a 40% deposit to buy a new home. New builds are exempt from the central bank rules.