Nepalese and Bhutanese migrants are being offered New Zealand citizenship in return for a fee.
The Department of Internal Affairs says the caller tells people he is from the department's Asian Minority Group, which does not exist.
The caller tells people that he can give them citizenship if they pay money via Western Union to Nepal for document transfer fees.
Internal Affairs says the caller appears to know detailed information about the families he's ringing.
Regulatory and compliance operations general manager Maarten Quivooy says the department received several calls on Friday about the scam.
He says one person has already made two payments worth almost $1500.
Mr Quivooy advises people contacted by the scammer not to pay any money and to contact the police if they already have.