Prime Minister Malcolm Turnbull will assume the Agriculture portfolio in Mr Joyce's absence.
Joyce claimed he wasn't aware he held New Zealand citizenship and has since renounced it.
Prime Minister Malcolm Turnbull has also been among those to previously assure the Australian people that Joyce is "qualified to sit in the house and the High Court will so hold".
Turnbull confirmed that a by-election would be held in Joyce's seat on December 2.
The fate of Deputy Prime Minister Barnaby Joyce is most crucial to the government in an unprecedented political crisis.
Four of the other six senators were also ruled ineligible from sitting in parliament, including government minister Fiona Nash, who inherited British citizenship through her father.
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The disqualified senators will be replaced by members of their own party without an election, meaning the balance of power will only be affected by Mr. Joyce's situation.
"The decision of the court today is clearly not the outcome we were hoping for but the business of government goes on", Turnbull told reporters in Canberra. He was born to Cypriot- and Greek-born parents and checked with both embassies to ensure he wasn't a citizen of those countries.
Contentious decisions made by ineligible ministers could be challenged in the courts.
All except one said they did not know they were dual citizens when they stood for parliament.
Members of Australia's national parliament can't be citizens of another country, according to section 44 of the country's constitution.
The lawmakers were exposed as dual citizens as media scrutiny escalated after Ludlam declared in July that he had been illegally elected three times over a decade.
The government had unsuccessfully argued in court that the phrase in the law "is a subject or a citizen...of a foreign power" should only refer to a person who has voluntarily retained that status.