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Mr Joyce told parliament on Monday the New Zealand High Commission had contacted him last Thursday with the "shocking" information.
"On the basis of preliminary advice from their department of internal affairs - which had received inquiries from the New Zealand Labour Party - they considered I may be a citizen by descent of New Zealand," Mr Joyce said.
Under section 44 of the Australian Constitution, anyone who holds dual citizenship is ineligible to sit in parliament.
Mr Joyce - whose eligibility will be referred to the High Court - won't be stepping aside from cabinet, unlike his Nationals colleague Matt Canavan who discovered his mother signed him up for Italian citizenship.
The Nationals leader told parliament he was born in Tamworth in 1967 to an Australian mother and was fifth generation Australian.
"My father was born in New Zealand and came to Australia in 1947 as a British subject. In fact we were all British subjects at that time," he said.
"The concept of New Zealand-Australian citizens was not created until 1948.
"Neither my parents nor I have ever applied to register me as a New Zealand citizen. The New Zealand government has no register recognising me as a New Zealand citizen."
The Sydney Morning Herald reported Mr Joyce's father James Joyce was born in Dunedin in 1924.
The government has received legal advice from the solicitor-general which suggests Mr Joyce would not be found to be disqualified under section 44 of the constitution and would not have to resign as the Member for New England.
But in any case he asked the government to refer him to the High Court.
The prime minister has asked that Mr Joyce remain deputy prime minister and continue his ministerial duties.
According to the NZ government passport website: "If you were born overseas and at least 1 of your parents is a New Zealand citizen by birth or grant, you are an NZ citizen by descent. To get yourself an NZ passport, you need to register your citizenship."
If Mr Joyce is found to be ineligible, the government - which holds a one-seat majority in the lower house - would be forced into a by-election.
The High Court is now considering the futures of five MPs: Mr Joyce, Senator Canavan, former Greens Scott Ludlam and Larissa Waters and One Nation senator Malcolm Roberts.