Cabinet minister Mitch Fifield will be referred to a parliamentary committee over what he knew about former Senate president Stephen Parry's citizenship status.

A motion moved by Greens leader Richard Di Natale passed the Senate with the support of Labor on Tuesday, directing the privileges committee to check whether Senator Fifield followed the ministerial code of conduct after learning of Mr Parry's possible dual citizenship.

Senator Fifield has admitted speaking with Mr Parry over concerns about his eligibility in August, weeks before the High Court disqualified five senators.