Scammers posing as power company staff are calling elderly people, demanding money for unpaid bills.
In the past week, two people in Queenstown and one in Christchurch had significant amounts of money taken from their bank accounts, police said.
Collectively, tens of thousands of dollars was lost.
In some cases, scam callers threatened to cut off the power immediately if payment was not made.
The caller then arranged for a bank "representative" to speak to the victim, persuading them to provide account details and passwords for payment.
Police said they appeared to hack victims' email addresses to get personal information before calling with demands.
Most of the cases reported to the police were from bank customers with an Xtra email account.
The Bankers Association first reported the scam on Thursday.
It was likely the money was transferred overseas shortly after it was taken.
Police were working with banks to identify the offenders and ascertain whether the stolen money could be recovered.
Police advised people to hang up if they were threatened by a caller claiming to be from a company.
"The IRD or any other government agency, police or a crown entity will not threaten someone," police said.
"Don't trust anyone who calls you and asks for financial information such as your account details and password."
Anyone who believed they may be a victim of the scam, or who received a call similar to the ones described, was advised to contact their bank and, if money had been withdrawn without authority, contact police.