The censure motion notes that Morrison undermined responsible government for failing to inform parliament or the public.
It follows the release of the report by the inquiry into the secret ministries scandal by former High Court judge Virginia Bell.
The report said it was “unnecessary” for Morrison to appoint himself as the secret minister for finance and health.
Bell concluded the secrecy around the ministerial appointments was “apt to undermine public confidence in the government”.
“Once the appointments became known, the secrecy with which they had been surrounded was corrosive of trust in government,” she wrote.
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Morrison defended his actions in a statement on Facebook, saying there were made to “best advance and protect Australia’s national interests and the welfare of the Australian people”.
The last time an MP was formally censured in federal parliament was in 2018.
Liberal MP Bridget Archer has announced she will break ranks with her party to support the motion.
Earlier the Coalition stated it will not support the motion against Morrison, who remains in parliament as the member for Cook.