That fund will also apply to those who are highly talented in an area such as sports or music for whom the extra funding can help develop that talent.
Ms Bennett said the payments would help take some of the pressure off the carers, many of whom were doing tough jobs on limited incomes.
About 12,400 children are cared for by extended family and other carers.
Although the carers do receive the Unsupported Child Benefit or Orphan's Benefit, they have not received many of the same allowances as foster parents.
The funding entitlements were decided on by a working group and accepted by Ms Bennett.
The first payments will apply from the start of the school year in January.
In its first year, the January payments will range from $250-$400 and will be scaled up to the full $400 - $550 over time.
NZ First MP Tracey Martin said she welcomed the extra support for carers but it did not relieve the disparity between foster parents and kin carers in other areas.
Ms Martin has a members' bill to extend foster parent entitlements - such as clothing and gift allowances - to kin carers which is currently in select committee.
She was included in the advisory group which developed the proposals for the $35 million extra funding and said it would apply to both foster and kin carers.
She said she hoped that announcement would not mean the Government believed her bill was now redundant.
"My concern is that now the National Government and people will think kin carers don't need more support and therefore they will kill my bill. But this particular support is for all orphans and unsupported children, whether they are in kin care or foster care. So the anomaly that my bill is trying to address still remains. This does not solve the disparity that is still around the clothing allowance.''
She said support for carers of children with extra needs was welcome, saying in one instance a grandmother caring for an autistic grandchild was unable to get funding for a gate she needed. "There needed to be a fund for that out of the box stuff. I do think flexibility was needed.''