First Minister Mark Drakeford has vowed to take action after concerns were raised about anti-bullying procedures in the NHS.
A group looking at the impact of Covid-19 on black, Asian and other minority ethnic (BAME) groups found people may have a fear of negative consequences if they use the policies.
It suggested the policies were not fit for purpose.
"This is clearly unacceptable", Mr Drakeford's said in his response.
He said he would take "coordinated action across NHS Wales to implement the recommendations... designed to tackle these experiences".
The first minister called on leaders in all areas of life in Wales to "drive racism out of our country", and vowed to create "a lasting legacy for Wales where there is fair treatment and advancement for all".
A report from the group said there had been a "lack of action" on race equality.
BAME people are nearly twice as likely to die with coronavirus as white people in Wales and England, according to statistics from the summer.
The comments about anti-bullying policies were made in a response by the first minister to the report of the Socio-Economic group, which was published in the summer.
Mr Drakeford said: "Within the NHS in Wales there are policies in place to support individuals to raise concerns in the workplace and to address issues where they have experienced bullying and harassment.
"The work of the Socio-Economic Group suggests that the lived experience of some black, Asian and minority ethnic members of the workforce means that these policies are not fit for purpose, and individuals may not feel confident to use the policies for fear of negative consequences.
"This is clearly unacceptable and we will work with social partners and black, Asian and minority ethnic members of the workforce to explore this evidence and take coordinated action across NHS Wales to implement the recommendations of the group designed to tackle these experiences."
The Welsh Government response said the report had been accepted "in its entirety".
The first minister agreed that it is "imperative to understand better the relationship between overcrowding which disproportionally affects some black, Asian and minority ethnic people and vulnerability to Covid-19".
Analysis of recent data found half of Wales' BAME population live in rented properties, compared to just under a third of the white population, and are more likely to live in privately rented properties.
It said a rapid review of previous research into race equality is being conducted, and a helpline has been set up to offer advice and information on a range of issues including work.
Mr Drakeford wrote: "I ask everyone to take a stand against inequality wherever and whenever they see it or experience it."