The baby is believed to have been a newborn, authorities said. An autopsy will be carried out tomorrow.
Police were first called to the Onehunga facility on Monday night. The investigation has continued through today, including efforts to identify the child's mother.
"We have already made inquiries with hospitals and will continue to work closely with them," said Detective Inspector Scott Beard.
Beard said police were "extremely concerned" for the welfare of the mother, who may need urgent medical attention.
Police have begun examining CCTV footage from the site, but Beard warned there is a "significant amount of work to undertake".
"These types of investigations can be extremely complex," he said.
"We have teams of specialist staff and this will be treated sensitively and with respect."
The private recycling facility in Onehunga is one of 120 owned by international company Visy throughout New Zealand, Thailand and Australia.
The company says its Auckland facility handles 30 per cent of kerbside recycling in New Zealand. It also accepts material that is dropped off, according to Auckland Council.
Calls to Visy's Onehunga site went unanswered this afternoon.
* Anyone who may have information about the incident is asked to contact police at 105, quoting file number 210816/2825, or to contact Crime Stoppers anonymously at 0800 555 111.
