The assistant health minister, David Gillespie, is the owner of a small shopping centre in Port Macquarie.
Inside the centre is an outlet of Australia Post, which is a government-owned corporation.
Labor believes that arrangement breaches Section 44 of the Constitution, which says federal politicians are not allowed to have a financial interest in the Commonwealth.
If a court challenge succeeded and Mr Gillespie were disqualified, it would trigger a byelection in the seat of Lyne, which could threaten the Turnbull Government's one-seat majority.
Acting Labor leader Tanya Plibersek says the Nationals MP does have a conflict of interest.
"We are not sure whether Dr Gillespie is actually, constitutionally, able to sit in the House of Representatives. Whether he was properly elected, because of his conflict of interest."
The Labor challenge will argue for Dr Gillespie's disqualification under similar grounds to those that saw former Family First senator Bob Day ruled invalidly elected earlier this year.
Section 44 is designed to make sure MPs cannot profit from government contracts while they are sitting in Parliament.
Ms Plibersek accuses the government of deliberately ignoring the matter because it is reliant on Dr Gillespie's vote.
"When it is one of their own in the House of Represenatives, when they are relying on this one vote, they are refusing to examine any potential conflict of interest and they are refusing even to respond to Labor's correspondence."
Mr Gillespie's office told SBS the MP will not be commenting at this stage.
But Foreign Minister Julie Bishop has rubbished the legal challenge.
"It sounds like yet another Labor stunt. It sounds like another attempt by Labor to disrupt and distract from the Government's policies that are clearly being effective. We're clearly able to get our legislation through the Senate and it sounds like another Labor distraction. It comes down to a question of remoteness of interest. But we'll wait to see what detail Labor intend to come up with."
Nationals leader Barnaby Joyce says his colleague Dr Gillespie is confident in his independent legal advice that he does not have a constitutional conflict.
Anne Twomey is a professor of constitutional law at Sydney University.
She told Sky News a successful challenge is unlikely.
"The idea of having a shopping centre and then having somebody in the shopping centre that you've let something to, then sublet to the Commonwealth, is reasonably remote. Unless there is some kind of extra influence involved that involved him as a Member of Parliament pressuring the government to somehow take a lease in his shopping centre then it's probably - it's more likely than not that it's on the side of being reasonably safe."
If the challenge succeeded and resulted in a by-election, the government would be likely to win the safe Nationals seat of Lyne again.
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