The scammers have been using numbers which show up as the Immigration Contact Centre, but with a slight variation in the digits.
The callers claim to be calling from Immigration New Zealand (INZ) and tell the person there has been a problem with the processing of their visa or arrival card information and demand a sum of money.
The scammers want the money transferred into a Western Union account or they will face serious consequences including deportation.
The callers were aggressive and authoritative, said the Ministry of Business Innovation and Employment, and often had details about the person they were speaking to, which made the call seem genuine.
Over a lakh Indian-origin people are residing in New Zealand.