Up to 12,000 families have already applied for money to help pay for childcare since the new National Childcare Scheme opened three weeks ago.
Almost 8,500 awards have been made to parents so far.
Every parent is entitled to some financial assistance, but the amount depends on personal circumstances.
Children's Minister Katherine Zappone said she is aware the subsidy will not amount to much for some families.
Ms Zappone said: "I understand it's not enough but it's a whole lot more than we've been able to do in the past.
"7,500 children are getting access for the first time under the NCS and 40,000 more families are getting increased subsidies.
"As I said before though, it's a base, it's much easier to invest and much easier to receive the subsidies with the National Childcare Scheme."