Labor wants Communications Minister Mitch Fifield referred to the parliament's privileges committee over concealing information about his Liberal colleague Stephen Parry.
Mr Parry resigned his role as Senate president and exited the parliament on November 2 over his dual citizenship.
Senator Fifield is understood to have known about Mr Parry's concerns about his eligibility since August, but kept it secret.
Labor leader Bill Shorten has written to Prime Minister Malcolm Turnbull asking that Senator Fifield, along with any other member or senator who was also in the loop, be referred to the privileges committee over the "cover-up".
"As a matter of principle, it should be incumbent on all members of parliament to not be complicit in concealing the ineligibility of another member," Mr Shorten wrote in a letter released on Thursday.
"I believe this is a most serious lapse of judgment."
