Figures obtained by RTÉ News show there are 1,700 people in direct provision who are sharing a bedroom with one or two non-family members.
This is despite advice from Chief Medical Officer Dr Tony Holohan, who said if someone is sharing sleeping quarters with people who are not part of the same family it is not possible to social distance.
Figures show that up to 30 April there were nine clusters of Covid-19 in direct provision centres across the country.
There were 62 cases of coronavirus among residents, 11 of which have involved hospitalisation.
The Irish Refugee Council said the number of cases of the virus increased significantly over the weekend.
The organisation has also raised concerns about the 1,700 residents in direct provision who are sharing a bedroom with one or two non-family members.
The Department of Justice said it had been directed by the HSE National Social Inclusion Office that non-family members sharing a room in centres are considered to be a household during the Covid-19 crisis and should implement social distancing measures on the same basis.
It also said there are 7,700 residents in direct provision and it has implemented a policy of a maximum of three non-related people per room.
The chief executive of the Irish Refugee Council has said it is very concerned that 1,700 people in direct provision are sharing spaces with non-family members, saying this is in contravention of public health guidelines.
Speaking on RTÉ's News at One, Nick Henderson said that it is nearly seven weeks into the pandemic and people in direct provision are still having to share "intimate spaces" including bedrooms, washing spaces and canteens with non-family members.
Mr Henderson said that the IRC has written to the HSE's social inclusion department last Friday to raise concerns about a statement which "unintentionally or not" means that people who may only share the characteristic that they are both claiming asylum are now deemed to be a household unit and are therefore not being subject to the same guidance of the Chief Medical Officer.
He said the organisation has received legal advice from a barrister which informs it that Ireland has an obligation to ensure that people can have space to social distance themselves.
He said this legal advice says that people should be given the provision of single or household occupancy accommodation as an essential measure to ensure social distancing and limit the spread of the virus.
Mr Henderson said it "has unfortunately taken a pandemic" to highlight the need to move away from the current system of direct provision, to end the system and implement an alternative system.
He said people waiting on asylum applications to be considered have a right to privacy and space where they can live including own-door accommodation for families.
He noted the Green Party has made it a condition of their involvement in a programme for government.