The policy was one of the key recommendations by the New Zealand Nurses Organisation in its submission to the Government's Green Paper on Vulnerable Children.
The strategy was backed by teachers' unions.
Mrs Turei said that too often New Zealand children were too sick or hungry to learn. The nurses would not be a replacement for doctors, but would be a first port of call for kids at poorer schools.
The Greens co-leader said that the policy was just one part of fighting child poverty, but it went some way to mitigating intergenerational poverty.
She said nurses already did a "fantastic" job in low decile secondary schools and some primary schools. But Greens felt that schools should not have to use their operations grants to fund this health care service.
Providing schools with nurses was expected to help to pick up symptoms of skin infections or rheumatic fever, which often lead to avoidable hospitalisations.
Treating rheumatic fever in New Zealand cost around $40 million a year.
At present, all children were eligible for a public health checkup before entering school.
And by the end of 2013, decile one to three secondary schools will have funding for a nurse, mostly to deal with mental health issues.
But Greens said there was no national framework for a health service system based in primary schools.
The policy would require 280 new school nurses, who would care for children in 650 schools which were not currently funded.
More than half of the $30 million would go towards nurses' salaries, and the remainder would cover medical costs, diagnostic tests, and administration costs.
The jobs were expected to be taken by experienced nurses, with the policy allowing for salaries of around $60,000 - a similar pay cheque to a senior nurse at a hospital.
A paper released with the policy said that 20 percent of graduate nurses were unable to find jobs in New Zealand.