The Department of Justice has confirmed to RTÉ News that an estimated 20 people have been refused accommodation in direct provision centres over the past two weeks because they are at capacity.
A number of asylum seekers have been left homeless as a result and at least one has been forced to sleep on the streets.
The Department of Justice said the number of people arriving in Ireland applying for international protection has increased over the past number of months.
It said 20 people were refused accommodation in the direct provision system over the past two weekends and were referred to homeless services.
Direct provision centres across the country are operating at nearly full capacity due to ongoing delays in the system and difficulties moving refugees into long-term rented accommodation.
The Irish Refugee Council said asylum seekers were not getting the support they need, which it said was a breach of EU and Irish law.
The Reception and Integration Agency, the State body responsible for running the direct provision system, said women and families were being prioritised and it said it was working to sort the problem out as soon as possible.
Figures from the agency show that in July 2016, centres were operating at just under 80% capacity, but that figure had risen to 97% in July of this year.
The Irish Refugee Council has described the situation as "unprecedented".
The council's CEO, Nick Henderson said it could have serious implications for the individuals and the system of granting asylum to those entering Ireland.
Mr Henderson said the failure of the Government to provide accommodation to asylum seekers breaches EU and Irish law.
He also said that the situation was predictable given the increasing pressure on the capacity of these centres over the past two years.
Mr Henderson said there were serious implications for the system if the State does not know where those who are seeking asylum are located because they cannot give them the financial, medical and legal supports provided by the Direct Provision system.
Minister for Justice Charlie Flanagan said he was keen to ensure that Ireland's obligations in relation to asylum seekers are fully complied with.
He said he would not comment on individual cases but that everyone is offered accommodation "of one form or another" and that there are "great challenges" in the system of direct provision due to the fact that people arrive to Ireland to seek asylum spontaneously, without notice.
Additional reporting Samantha Libreri