Under section 44 of the constitution, anyone who "is under any acknowledgement of allegiance, obedience, or adherence to a foreign power" can not stand for parliament.
Senator Ludlam said he didn't have the money to pay back his salaries and allowances.
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.
In a post on Twitter, Ludlam said he was "personally devastated" when he learned about the "avoidable oversight" and apologized "unreservedly" to his constituents for his mistake.
The experienced barrister is single-handedly responsible for obtaining the proof that Senator Ludlam still holds New Zealand citizenship and is ineligible for politics.
Greens senator Scott Ludlam is leaving federal parliament after finding out he was improperly elected more than a decade ago.
The Greens co-deputy leader is the third senator to fall foul of the Consitution in this term of parliament, with South Australia senator Bob Day resigning in November a year ago after his building company went into liquidation.
Ludlam released a statement on Twitter on Friday afternoon, saying he had "recently discovered" he still held New Zealand citizenship.
It then took Senator Ludlam's office several days to contact the High Commission in New Zealand and verify the information was correct. He became a naturalised Australian as a teenager.
'It is entirely my responsibility - it wasn't the way I was hoping to go out'. I'll really miss it, but there are other ways to make trouble.
"(That) is my recollection as the way it's dealt with in the past", he said.
The ABC's election analyst Antony Green said he thought it was unlikely Mr Ludlam's salary would be clawed back.
'He has been a strong representative for the people of WA and the nation on a range of issues'.
Speaking to The Weekend Australian, Cameron insisted that he was not politically motivated, and that he merely acted as "a citizen" with a "keen interest" in the workings of the Australian Constitution.
Mr Ludlam's position will be filed by a recount of ballot papers from the 2016 election, leading to the possible election of 22-year-old Jordan Steel-John who was third on the Greens Senate ticket.
Steele-John gave up his own British citizenship to first run for the seat of Fremantle as an 18-year-old, the Guardian Express reported last year.
In January, the High Court ruled that former One Nation senator for Western Australia Rod Culleton's election to parliament was invalid because he had been charged with stealing a $7.50 truck key.