The driver said he understood the risk was small but questioned why he needed to be exposed to it at all.
"What kind of isolation is my taxi," he said.
The man said nobody had briefed taxi drivers about the risks or what to do and he said if he complained at his company, they would just get another driver.
"I don't know what to do now - seriously," he said.
"I could put my family, the other passengers at risk and I wouldn't know."
Taxi Federation executive director John Hart said members should look to invite a Ministry of Health official to brief drivers about the situation.
Drivers had earlier raised concerns about the situation but this had eased when foreigners who had transited or visited China were temporarily banned from entering New Zealand, he said.
He said drivers could consider wearing masks and carrying disinfectant.
But he also said it would be unacceptable if some drivers refused to pick up Chinese customers.
"Anyone could have the virus," Hart said.
While passengers were having their temperatures checked on flights out of China and Hong Kong, only those who volunteered to do so were being checked in Auckland airport.
Yesterday, the Ministry of Health set up a coronavirus helpline and registry for those in self-isolation.
A National Telehealth Service said many people had already called the helpline to register themselves as being in self-isolation and with questions about the virus.
More details would be released at a press conference tomorrow, he said.
Meanwhile 1175 people had called health authorities since January 30 "specifically to discuss novel coronavirus".
"At this stage no one we have spoken to has met the Ministry of Health clinical criteria for a novel coronavirus test and been advised to visit a medical practitioner," National Telehealth Service chief executive Andrew Slater said.
The Herald has sought comment from Auckland Airport and the Ministry of Health about whether they had briefed airport staff and taxi drivers about the risks but was yet to receive a reply.