These families are no longer entitled to monthly child benefits of €131.60 or lone parent payments of €134.80.
They are now left with weekly payments of €19.10 per adult and €9.60 per child to live on. This is on top of direct provision, including room and board.
"Because the parents are not allowed to work, child benefit payments are the principal financial means of preventing the children of asylum seekers from becoming utterly destitute," said Ray Dooley, chief executive of Children's Rights Alliance.
"Denying child benefit assistance to these children represents a flagrant violation of their rights under international human rights treaties, including the UN Convention on the Rights of the Child, which Ireland has solemnly pledged to uphold."
The "habitual residence test", which was introduced by Minister for Social and Family Affairs Mary Coughlan, restricts access to social welfare claimants from the 10 new EU members. Anyone entering Ireland from these states has to be resident for two years to qualify for those payments.
Fine Gael spokesman on social and family affairs, Michael Ring, said Ms Coughlan has "moved the goalposts" by including asylum seekers in the test.
"This is very underhand. It is yet another mean move by Mary Coughlan. This government is again showing its right-wing credentials," he said.
Itayi Viriri, policy officer with the Irish Refugee Council, called on the minister to exempt asylum seekers from the test and to re-examine the whole system of direct provision.
A Department of Social and Family Affairs spokeswoman said the policy applied to everyone who did not satisfy the habitual residence condition.
She added: "The State is looking after asylum families. Their needs are being met by the direct provision arrangements. If someone is not an asylum seeker and is not entitled to work, they may avail of the option of repatriation."