Both had now fully recovered and suffered only mild symptoms.
Two potential modes of transmission were being considered: through unprotected sex, or the woman being bitten by an infected mosquito brought into the country in her partner`s luggage.
There was limited scientific evidence to suggest the virus could be sexually transmitted, said the statement.
The couple`s property was under surveillance for any exotic mosquitoes, but none had yet been detected.
The risk to the wider public was extremely low and the species of mosquito that could spread the virus was not native to New Zealand.
In February, the ministry said that eight Zika cases had been confirmed in New Zealand this year, all affecting travellers who had recently been in the South Pacific nations of Tonga, Samoa and American Samoa.
In 2014, New Zealand had 57 Zika notifications, and last year six.
More about:
