The court move reintroduced uncertainty into a political landscape that has been turbulent in recent years, with four different prime ministers serving since 2013.
"The decision of the court today is clearly not the outcome we were hoping for but the business of government goes on," Prime Minister Malcolm Turnbull said in Canberra after the ruling was handed down.
Joyce, the leader of the rural-based National Party, is Australian-born but found out in August he automatically acquired New Zealand citizenship through his father. He told reporters in Tamworth, a city in his New England seat, that he was "always prepared for this outcome".
"I had no reason to believe that, you know, I was a citizen of any other country that Australia. That is the way it is... Now I am going to make sure that I don't cry in my beer."
The 50-year-old has since renounced his New Zealand citizenship, allowing him to run in the by-election.
Independent MP Cathy McGowan said in a statement she would "continue to supply confidence and support to the government," giving the coalition room to breathe in the lower House of Representatives.
The deputy's position is expected to be kept vacant ahead of the by-election, with Foreign Minister Julie Bishop set to take on the duties if Turnbull travels overseas, according to local media. If Joyce loses the by-election, the coalition could keep ruling as a minority government if it receives the support of independent MPs on budget matters and on votes of no confidence.
Of the so-called "citizenship seven", only Nationals senator Matt Canavan and independent senator Nick Xenophon were cleared for parliament. The others, who are also upper house senators; the Nationals' Fiona Nash, the Greens' Larissa Waters and Scott Ludlam and One Nation's Malcolm Roberts were like Joyce also ruled ineligible.
Canavan, who left cabinet and his role as resources minister after finding his mother signed him up to Italian citizenship in his 20s, resumed the job after being sworn back in.
The dual citizenship rule was originally inserted into the 1901 constitution to ensure parliamentarians were loyal solely to Australia. However, critics say it is out of step with the modern reality of the country, where 50 percent of the population are either foreign-born or the children of immigrants.
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