The airline said on Monday that China denied the plane landing permission due to an administrative error.
New Zealand's Minister for Transport Phil Twyford said his staff told him of the diversion once the issue became public.
"As is required, the application includes a list of destinations the airline operates to, including Taipei", Air New Zealand said, without elaborating.
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.
Air NZ flight 289, which was bound for Shanghai, was forced to turn back to Auckland after several hours in the air because Chinese authorities deemed that its application to land in China contained wording that indicated Taiwan is an independent country, according to sources cited by Stuff.
"A technicality meant the particular aircraft operating this service did not have Chinese regulatory authority to land in China", the airline said.
New Zealand Prime Minister Jacinda Ardern says a flight from New Zealand to China was turned back for administrative reasons and the incident has no bearing on the relationship between the two nations.
There is no doubt that the relationship is in a hard state, and many in media and foreign affairs circles are on the lookout for any sign that China is punishing New Zealand.More news: Trump to Ban Huawei Tech in US Wireless Networks
The incident has created a potential headache for New Zealand's government, which has recently suffered frosty relations with Beijing.
"Air NZ wishes to sincerely apologise for the return and subsequent retiming of your flight, NZ289". "Our relationship with China is a complex relationship, and sometimes, it will have its challenges", she told TVNZ.
Exactly how much the difficulties in the relationship with China can be blamed on the Government is hard to know.
Ardern cancelled her first planned state visit in November 2018 because both parties were too busy.
The United States, Australia and New Zealand have all blocked or limited the use of Huawei equipment as the company eyes a global toehold for 5G technology.
Ardern was scheduled to visit China early this year but the invitation has been put on hold.
New Zealand yesterday said Beijing had postponed an event to launch the China-New Zealand Year of Tourism 2019 in Wellington next week.