"There is limited scientific evidence to suggest the virus can be sexually transmitted - it's very rare," Dr Mackie said.
"Surveillance of the property is being carried out to check for any exotic mosquitoes. At this stage, none have yet been detected."The risk to the wider public is extremely low. The species of mosquito that can spread Zika are not native to New Zealand."
The ministry announcement did not say where the couple who tested positive for Zika lived, or which Zika-affected country the man had been to.
Dr Mackie said the local public health service was continuing to investigate how the woman became infected.
No further details on the cases would be released to protect the privacy of the individuals involved, the ministry said.
Auckland University infectious diseases expert Dr Siouxsie Wiles said an infected mosquito in luggage was "improbable" and sexual transmission of the disease was more likely.
"There are now a handful of cases documenting possible sexual transmission of the virus. They have all been cases of transmission from men to women; so far there have been no cases of transmission from women to men.
"There has also been a case of a man who didn't transmit the Zika virus to his partner but the virus was detected in his semen."
Dr Wiles said sexual transmission of the virus was not the main route of infection.
"It is still quite rare," she said.
"It is important to note that in New Zealand we don't see the kind of sustained spread or transmission is happening in countries like Brazil. We don't have the mosquitoes that carry the virus here in New Zealand."
Health authorities advise men travelling from an infected country who fall ill to either abstain from having sex or use a condom.
"The advice on how long you should wear a condom or abstain from sex for varies. The WHO says four weeks, but the UK is saying up to six months. The reason for this is because at this stage they have no idea of exactly how long a man with Zika infection is likely to have the virus in his semen," Dr Wiles said.
• Anyone wanting more information should contact Healthline on 0800 611 116 to speak to a registered nurse. The Healthline service has access to interpreters for 44 languages, 24 hours a day, 7 days a week.