Calls to the civil aviation administration were not answered.
New Zealand's Minister for Transport Phil Twyford said his staff told him of the diversion once the issue became public.
Daily Mail Australia has contacted Air New Zealand for comment.
Last year, New Zealand issued a defence policy statement in which it said China's rising influence in the South Pacific could undermine regional stability, and alluded to tension in the disputed South China Sea, sparking complaint from China. DPA added that that the aircraft returned to Auckland about five hours after taking off and did not have permission from the Chinese authorities to land.
In a statement, Air New Zealand said a Boeing 787-9 Dreamliner that joined its fleet late past year was not yet certified to fly to China but was "unfortunately assigned" for the Shanghai flight.
China has a history of demanding worldwide airlines not refer to Taiwan's independence or nationhood on its websites or promotional material, and in the past has urged Qantas, Air Canada and others to change how it refers to the island.
China refuses to have diplomatic ties with governments that recognise Taiwan and has been cracking down on airlines that do so.
New Zealand's national carrier admitted a registration mistake turned back a flight to China over the weekend, prompting Prime Minister Jacinda Ardern to say Monday that politics were not involved.
The incident has created a potential headache for New Zealand's government, which has recently suffered frosty relations with Beijing.
The Boeing 777-219 Flight NZ296 from Auckland was due to land at the Faleolo International Airport at 2:10pm (Samoa Time) this afternoon and for passengers to disembark. "Is it part of the ongoing deterioration in relations between this NZ Govt & China?"
"Our relationship with China is a complex relationship and sometimes it will have its challenges", Ardern told TVNZ in an interview.
Ardern cancelled her first planned state visit in November 2018 because both parties were too busy.
"I have been issued with an invitation to visit China, that has not changed".
New Zealand political journalist Richard Harman speculated on his website Politik that the rejection of flight NZ289 was China reacting to New Zealand's decision to ban Chinese telco Huawei from supplying 5G to New Zealand telco Spark.
New Zealand yesterday said Beijing had postponed an event to launch the China-New Zealand Year of Tourism 2019 in Wellington next week.