Specialist foam equipment was on site, Mr Phillips said.
Managing Director of Stolthaven Australiasia that owns the storage facility, Graham Catley, said the source of the leaked oil, that is heated so it can be circulated through pipes around the Marstel Terminals building, was being investigated.
"You can sometimes get a pinhole leak in a pipe and it drips, which it appears has happened here, and for some reason that has ignited and we have had a very, very small fire which we have extinguished with our own fire extinguishers."
Mr Catley said the company, which only had about eight employees at the large site at one time, had strict response protocol that were followed.
"We have got to take everything extremely seriously," he said.
The plant was evacuated but there was no severe damage.
Mr Phillips said the Fire Service received multiple calls from people in downtown Auckland reporting smoke.
There were no reports of injuries.