Approximately 40 adults and 45 children in the State-owned Johnston Marina direct provision centre in Tralee, Co Kerry, one of three outlets in the town for people seeking asylum, are refusing food provided by the centre.
The Johnston Marina currently houses 94 people.
The families are now buying their own food out of their €19.10 weekly allowance for adults and just over €9.50 for children.
A spokesman for the striking residents, Dr Hameed Alshakaty, a cardiologist from Iraq, said: "Food is one problem: the main problem is management don't respect us."
He is hoping to get a permit to work in Ireland and says he is currently living in a small room designed for two people in the Tralee centre with his wife and three children.
He has lived in the hostel since June.
The protest began on Monday and would continue until the Department of Justice sent a representative to deal with the issue, he said.
Grainne Landers, of Tralee Refugee Support Services, said the Reception and Integration Agency knew of the problems at the Johnston Marina and the situation could have been avoided.
The agency said "it is satisfied that the company operating the accommodation centre have provided a very high level and quality of service to residents".