Joyce was one of five lawmakers ruled ineligible Friday by the High Court in Canberra, but the only one from the lower house.
The Australian constitution bars citizens of foreign countries from serving in parliament. Joyce claimed he wasn't aware he held New Zealand citizenship and has since renounced it.
"It's a pretty simple story, we're off to a by-election (and) I put myself forward to the people of New England as a candidate," Joyce told reporters in his constituency, a rural part of eastern Australia, north of Sydney.
"I had no reason to believe I was a citizen of any other country but Australia."
Speaking Friday, Turnbull said it was "clearly not the outcome we were hoping for" but denied that his government faces any instability in the absence of Joyce.
"We have the support of a majority of members," Turnbull said. A no-confidence vote would require all independent and crossbench lawmakers to turn against the government.
In August, Turnbull accused the then opposition New Zealand Labour Party of working with its Australian counterparts to "undermine the position of the deputy prime minister and the government of Australia."
What's the problem?
Following the court's decision Friday, Turnbull said his government will refer the matter to electoral authorities, to consider "whether any changes to section 44 should be recommended" or how election laws could be changed.
Turnbull said he wanted to ensure "in our multicultural society that all Australians are able confidently to stand and serve in our parliament."
Who is Barnaby Joyce?
He's also the nemesis of actor Johnny Depp, whose dogs, Pistol and Boo, Joyce threatened to euthanize in April 2016 after they were brought illegally into Australia.
Joyce told lawmakers in August he had discovered he was a New Zealand citizen, throwing his position in parliament into jeopardy.
CNN's Ben Westcott contributed reporting.