Media reports say a convoy of cars was ambushed near the city of Calabar in Cross River State on Wednesday morning.
The driver was killed and seven employees of engineering firm Macmahon were taken away on a waiting boat, reports said.
Kidnap-for-ransom is a longstanding issue in southern Nigeria, where gangs target expatriate workers.
Australian Prime Minister Malcolm Turnbull said the identity of the kidnappers was unknown at this stage.
"It is a very serious kidnapping, a very serious criminal assault, one person was killed and seven people have been kidnapped," Mr Turnbull said.
He confirmed that three Australians were among those kidnapped, along with a New Zealander who is a permanent resident of Australia. It is believed that at least two Nigerians were also kidnapped.
There has been some confusion over the exact number of people abducted by the 30 militants involved in the attack.
Nigerian Police Commissioner Jimoh Ozi-Obeh told reporters that police were working with the Nigerian Navy to ensure all victims were released unharmed.(BBC)