But the issue won't be tested in the High Court until later in August.
The deputy prime minister told parliament on Monday the New Zealand High Commission contacted him last Thursday to advise him he could be a citizen of that country by descent.
Under section 44 of the Australian Constitution, anyone who holds dual citizenship is ineligible to sit in parliament.
The Nationals leader was born in Tamworth in 1967 to an Australian mother and is a fifth generation Australian.
His father was born in NZ and came to Australia in 1947 as a British subject - a year before NZ citizenship was created as a legal concept.
"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," Mr Joyce said.
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.
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However, a spokesman for the NZ internal affairs minister Peter Dunne told AAP there was crown law advice Mr Joyce was a New Zealander.
"Under our law, as we understand, and it has been confirmed by crown law - they have had a look at it - yes, he is," the spokesman said.
Mr Dunne told Sky News he had received advice on Wednesday "that this is potentially a problem relating to Mr Joyce".
"The advice that I received was being checked by crown law. That was confirmed. At that point it was conveyed via the NZ high commissioner in Canberra to Mr Joyce directly."
Labor frontbencher Tony Burke told parliament Mr Joyce should stand aside from the ministry and the government should not accept his vote.
"We've never before in this parliament ... had to go to the High Court and say: 'Look, we're not really sure if there's a majority government in this country'," he said.
The High Court is now considering the futures of five MPs, with August 24 already set aside to hear cases involving Senator Canavan, former Greens Scott Ludlam and Larissa Waters and One Nation senator Malcolm Roberts.
Mr Turnbull has written to offer Mr Shorten "the opportunity to nominate any Labor members or senators whose circumstances may raise questions under section 44 of the constitution" so the parliament can also refer those matters to the High Court.
"The Australian people must have confidence in our political system and resolving any uncertainty is vital," Mr Turnbull said.
The government is believed to have been advised Mr Joyce has a strong case based on him not being on an NZ citizen list, his parents not having applied, his lack of knowledge and the fact he had never sworn allegiance to NZ.
