The risk index is likely to be introduced in 2019 or 2020.
Ms Kaye said what the risk index takes into account is to be finalised, but 16 draft factors include ethnicity, mother's average income, how old the mother was when the child was born, and whether the male caregiver is not the biological father. A school's funding would be based on the number of students with risk factors.
She gave a reassurance that no school would lose funding under the new system.
"I'm pleased to be able to confirm that no school, early learning service or ngā kōhanga reo will see a reduction in their funding as a direct result of this change," Ms Kaye said.
"In fact, we expect some will gain significantly."
The decile system, introduced in 2008, rates schools on a scale of 1 to 10, based on the socio-economic position of the student community.
Low-decile schools receive more Government funding than those with high deciles, but it's not a reflection of the quality of the education provided.