When asked if Mr Ludlam will have to pay back his salary from when he was first elected to the Senate, Mr Turnbull did not rule it out, saying the decision would be left to Finance Minister Mathias Cormann.
"I am personally devastated to learn that an avoidable oversight a decade ago compels me to leave my colleagues, supporters and my wonderful team", Mr Ludlam said in a statement.
The deputy leader of an Australian political party announced Friday that he was ending his nine-year career in Parliament because he had discovered he had technically never been a senator.
The experienced barrister is single-handedly responsible for obtaining the proof that Senator Ludlam still holds New Zealand citizenship and is ineligible for politics.
The barrister at Francis Burt Chambers contacted Senator Ludlam's office last week "as a courtesy" to let them know he was sending proof of the Greens politician's New Zealand citizenship to the Clerk of the Senate.
Ludlam, who was born in New Zealand and moved to Australia at the age of three, says he assumed his naturalisation removed his New Zealand citizenship, but that it had recently been drawn to his attention that he remained a New Zealand citizen.
Dual citizens are banned from holding office in the federal parliament under the Australian Constitution.
'This was my error, something I should have checked when I first nominated for preselection in 2006'.
He settled in Australia not long before his ninth birthday, before being naturalised when he was in his mid-teens.
The ABC's election analyst, Antony Green, wrote on Twitter that Ludlam's resignation would cause a recount and the number 3 Greens candidate, Jordan Steele-John, would be elected. I expected the human headline may not have done it and Mr Ludlam would have done it, but it was the other way around.
Fellow parliamentarians paid tribute to him on Twitter, including Greens leader Richard Di Natale and Ludlam's co-deputy leader, Larrisa Waters.
"Scott has been an outstanding member of the parliament and of the Greens", he said in a statement.
The Australian Greens will continue to be strong advocates for a cleaner, greener and fairer Australia.
Mr Steele-John, who has cerebral palsy, had to give up his British citizenship to run for parliament back in 2013.
The dual citizenship means under the Australian constitution he can not legally be a member of the Australian Parliament.
The Senate and the Department of Finance had pursued former South Australian Family First senator Bob Day and former West Australian One Nation senator Rod Culleton for repayment of salaries and allowances.