A SECOND student has been infected with measles at a Steiner school in Perth, which is at the centre of a possible outbreak, following the resignation of the principal amid controversy over his anti-vaccination views.

The student was isolated at home and is not considered a risk to others, a Health Department spokeswoman told AAP.

The West Australian government issued a citywide alert last week when it emerged an unvaccinated year 10 student had returned from Italy with measles.

The department warned a substantial number of Perth Waldorf School's more than 400 students - possibly half - had not been vaccinated.

The school did not initially respond to a department offer to immediately provide vaccinations, prompting sharp criticism from the Australian Medical Association and the suggestion taxpayer funding be cut from schools that similarly did so.

The school then revealed in a letter published by staff and parents on its website that its principal Jean-Michel David had resigned.

Mr David stood as a candidate for the 2014 Victorian election on an anti-vaccination platform and specifically laws banning children not immunised from enrolling in kindergartens and child care.

"To impose or penalise those who do nothing wrong except not partake of government-imposed injections is mind bogglingly autocratic and has no place in a western democracy," he wrote at the time.

The school's acting administrator Mark Phillips said he would accept department nurses at the school and unvaccinated year 10 children were being kept at home this week.

Steiner Education Australia denies it opposes vaccination, saying it is up to parents, but Steiner alternative schools are known globally for having far higher rates of unvaccinated children than the general population and are considered at risk of measles outbreaks.

A US study published in the JAMA Pediatrics journal last month blamed the return of measles and mumps as a threat in developed countries on falling vaccination rates based on non-medical personal beliefs.