The workers are employed by Perth-based mining and engineering company Macmahon Holdings.
Mr Turnbull said the gunmen also shot dead one of the mining company's drivers during the attack near the capital of Cross River State, Calabar.
"We don't know at this stage the identity of the kidnappers and families in Australia are notified of course," he said.
"It is a very serious kidnapping, a very serious criminal assault, one person was killed and seven people have been kidnapped."
The New Zealander is a permanent resident of Australia.
