Mr Joyce - who was punted from office by the High Court last week - on Wednesday said other members of parliament needed to speak up immediately rather than wait to fall foul of the constitution.
For the past few months while the citizenship fiasco has unfolded, Parry has sat silent, choosing to keep doubts over his own status to himself, despite knowing his father was British-born.
Parry's resignation would be another major blow to the government, which is still reeling after Joyce was found to be in breach of the dual citizenship law.
"I will submit my resignation as both president of the Senate and as a senator for Tasmania to his excellency the Governor-General tomorrow", the Liberal Senator wrote in a letter to other senators, according to local media.
The Liberal senator from Tasmania sought advice from the UK Home Office after the High Court ruled on the eligibility of seven parliamentary colleagues.
Because my departure is rapid and an unexpected event, I will not have the usual opportunity to address you in the Senate one last time.
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His attorney, David Patton, has said he hopes "everyone lets the judicial process play out". "Mr. As the charges are federal, the government can override NY state's ban on capital punishment.
Given that Deputy Prime Minister Barnaby Joyce was booted from parliament after it was revealed he was a duel citizen of New Zealand. I wish to thank all of you as colleagues, many of whom I regard as good friends - from all quarters of the chamber - for your support and confidence in me.
Mr Parry said in a statement that he believes he was wrongly elected because of his status.
Former minister Eric Abetz said the fact that Senate President Stephen Parry had discovered after the court ruling that he had a potential problem showed the need for more checks.
Prime Minister Malcolm Turnbull said he is disappointed Stephen Parry didn't tell him about his dual citizenship sooner.
Meanwhile, despite the latest revelation, the government has yet again ruled out an audit of every federal MP to uncover who is and who is not a dual citizen.