The Australian government is working with Nigerian officials to get to the bottom of the kidnapping.
Australian Prime Minister Malcolm Turnbull says the Australian high commissioner in Nigeria is at the scene.
The families of those kidnapped have been notified.
The trio are said to be contractors for cement company Lafarge Africa, Reuters reported.
The group were attacked on the outskirts of Calabar in the early morning (about 4.30pm yesterday, NZT).
A spokeswoman for Lafarge said its contractor in Nigeria, MacMahon, had alerted Lafarge Africa that a security incident had happened on the road from Calabar involving some of its employees.
The Australian mining giant MacMahon was working with government security agencies to resolve the situation.
The New Zealand Government confirmed a New Zealand citizen and a number of Australians working for an Australian mining company had been kidnapped.
The Nigerian Government said it was throwing everything it could behind the operation to secure the release of a New Zealand man, four other expats and two Nigerians.
The group was kidnapped after their driver was shot dead as he was taking them to work.
They all worked for the Australian mining and engineering company Macmahon.
Nigerian Government spokesman Christian Ita said security services, the police and army were doing everything possible to ensure the release of the New Zealander and everyone else affected.
They knew where the group was being held, he said.
Christian Ita said it appeared a militant group was responsible but he was unaware of any demands for money.
The Government was hopeful the hostages would be released soon.
A witness told local newspaper, the Punch he was returning from his farm yesterday when he saw the kidnapping happen, near the Idundu Bridge, in the eastern part of the city of Calabar.
"These kidnappers came out from the bridge, shot the driver of the vehicle and took the victims away through the river.
"The vehicles conveying the expatriates and the two Nigerians were abandoned by the road-side with the dead body of the driver. From all indications, the expatriates were going to work at the Lafarge Holcim plant in Mfamosing.''
A spokeswoman for Cross River state police told the publication two of the men had since escaped, but she did not know their nationality.
The Ministry of Foreign Affairs and Trade said officials were in contact with the hostage's family.
A spokesman said the ministry continued to seek more information on the situation and was also in contact with Australian authorities as well as the mining company.
Given the sensitive nature of the situation the Ministry said it would not be commenting further.
A spokesman for Foreign Affairs Minister Murray McCully said the minister was receiving updates on the situation as it unfolded.
The kidnappers are yet to contact police.
An MFat spokesman said 25 New Zealanders are registered with the government in Nigeria.
The MFat website said as there was no New Zealand diplomatic presence in Nigeria, so the ability for the government to provide assistance to citizens was severely limited, particularly in regions where travel was advised against.
The Ministry of Foreign Affairs has Nigeria has a extreme risk rating because of the threat from terrorism, kidnapping and violent crime.
It advises against all travel in the north and against all tourist and other non-essential travel throughout the rest of the country.
It says there is a high threat of kidnapping throughout Nigeria, but particularly in the north, where most of the recent kidnappings had happened.
Expatriate workers at oil and gas facilities were at particular risk of kidnapping as the crimes were often financially motivated.
New Zealanders working in the northern states against Government advice were advised to seek professional security advice and take appropriate personal security measures at all times.
Another high-profile kidnapping involving a New Zealander was that of Mary Quin, who in 1998 was in a tour group that was taken hostage by armed and masked militants in Yemen.
Palmerston North-born Dr Quin, now a member of the board of Westpac NZ, was one of 16 tourists taken hostage by the group, who used them as shields in a gun battle between the Aden-Abyan Islamic Army and Yemeni troops.
Dr Quin managed to flee after she ripped an AK-47 from a kidnapper.
She later wrote the book Kidnapped in Yemen about her ordeal.
