Mr Small, who filled the Senate vacancy left by former finance minister Mathias Cormann in 2020, looked into his status after being queried by Liberal officials ahead of the May 21 poll.
Authorities confirmed on Thursday he had gained New Zealand citizenship through his father being born there.
Mr Small has since been granted a renunciation of any citizenship rights and will remain a candidate for re-election in third place on the Liberals' WA Senate ticket, behind frontbencher Michaelia Cash and government whip Dean Smith.
He tendered his resignation to the president of the Senate on Friday.
"Hopefully (a) temporary hiccup and if we win three seats, I'm back from 1 July," he told AAP.
Perth-born Mr Small said he had always been an Australian citizen.
When he was born, his mother was an Australian citizen and his New Zealand-born father was an Australian permanent resident.
"I had always understood that I had no entitlement to New Zealand citizenship based on the laws that applied at the time of my birth," he said in a statement.
"However, late last Wednesday 6 April, as part of preparations for the upcoming election, Liberal Party officials queried whether I may have an entitlement to New Zealand citizenship.
"Within 24 hours I took steps to engage with the New Zealand High Commission to clarify my status and, if necessary, to renounce any eligibility or right to New Zealand citizenship that I might have.
"Yesterday afternoon, Thursday 14 April, the New Zealand High Commission confirmed that I had been a citizen of New Zealand and, further to my application, granted a renunciation of any New Zealand citizenship rights."
Mr Small said while his ineligibility would need to be confirmed by the Court of Disputed Returns, it was appropriate that he resign immediately.
"Now that any questions around my eligibility have been resolved, I look forward to continuing to campaign across WA as a candidate for the Senate and to ensuring the Morrison government can continue to implement our plans for an even stronger Australia," he said.
A total of 15 MPs and senators, including Deputy Prime Minister Barnaby Joyce, were forced to resign in 2017 and 2018 after concerns emerged about their citizenship status.
Section 44 of the constitution bans dual citizens from sitting in federal parliament but a number of parliamentarians had not renounced their citizenship from other countries or were not aware they had it.
Mr Joyce, who was also deemed to have New Zealand citizenship by descent from his father, was among those re-elected after renouncing their foreign ties.
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