A Fair Work Commission (FWC) deputy president who railed against vaccine mandates will be barred from hearing workplace vaccination matters and will be excluded from full bench work until she completes training.

Deputy president Lyndall Dean last month likened vaccination mandates to "medical apartheid and segregation" and said the concept is "the antithesis [sic] of our democratic way of life and everything we value".

She made the remarks in a dissenting judgment in an unfair dismissal case involving a woman who was fired from her job at a nursing home for refusing to get a flu shot.

On Wednesday, it was revealed Ms Dean had also expressed support for a social media post that argued public-health measures implemented during the pandemic are akin to "Chinese-style totalitarian social control".

In response to the LinkedIn post, which also suggested the world is on the brink of a catastrophe on par with the Holocaust, Ms Dean commented "I fully agree".

FWC General Manager Murray Furlong told Senate Estimates on Wednesday that commission President Iain Ross had received a complaint in relation to Ms Dean.

"While the President does not have power to discipline members, he has certain powers to deal with complaints about members," he said.

Mr Furlong said the President wrote to Ms Dean directing her to "attend training on responsibilities and standards of professional conduct expected of a member of the commission".

"She will be excluded from all and any further full bench work at least until she's completed that training," Mr Furlong told Senate estimates.

"And she has disqualified herself on the grounds of bias from adjudicating disputes relating to workplace vaccinations in future."

Mr Furlong said Industrial Relations Minister Michaelia Cash had also been informed of the steps taken in response to the complaint.

When asked by Labor senators about the social media post, Acting Attorney-General Amanda Stoker said she did not agree with it.

"It's something I've seen for the first time now, it's not a view I share," she said.

Senator Tony Sheldon asked if she held concerns about the views being espoused by the commissioner.

"I don't know what the full suite of Ms Dean's behaviour has been like, and I think it would be it would be foolish to judge the entirety of a person's contribution in light of one article," Senator Stoker responded.

"But that said, I don't agree with what she has posted, and it sounds like the procedure that has been put in place by the commission to manage any perception of bias arising from it is appropriate."

Senator Cash announced Ms Dean's appointment to the commission in 2016.

"She is highly regarded as a workplace relations lawyer and brings high level analytical, negotiation and conflict resolution skills to this role, as well as a demonstrated capacity for complex decision making," she said in a statement at the time.

"I'm sure the skills and experience she will bring to the commission, including understanding the needs of small business, will assist the commission's work to ensure Australia has fairer and more productive workplaces."