However 30 to 40 people have been evacuated from nearby factories.
St John's Ambulance northern communications team leader James Ihimaera said it was increasingly unlikely any patients would be transferred to hospital with most injuries related to smoke inhalation.
No more patients were expected, he said.
Textile Products was set up in 1960 and has grown to employ 25 people, according to the company's website.
The company stores insulation materials.
Witness: 'It's pretty bloody gnarly'
Newstalk ZB said it understood workers smelt burning rubber and saw flames heading towards the roof of the factory.
Pete Marsden said he could see the smoke on the Southern Motorway.
"It's down by Waikaraka Park in Onehunga, I'm currently on the Southern Motorway right now, there's massive black clouds coming from the Onehunga area and they're going right across the motorway.''
He said the fire was similar in size to the fire that destroyed a Mitre 10 building last year.
Local man Sam de Court noticed the fire around 11.10am.
"Basically it is a big orange shed and there is a load of silos [nearby] that look like they hold gas or something.
"It's pretty bloody gnarly."
Zebra Car Collection worker Kim Gorman said thick black smoke from the "massive" fire was billowing over surrounding businesses.
The black clouds were about the height of a large power pylon near the site of the blaze, she said.
"They're just billowing up in the air over everything. It's huge. It's massive."
