Under the law, children over six can not be banned from school but their parents will be fined up to €500 (£425).
There have been protests over the law changes around vaccinations in Italy.
"Italy's measles vaccine coverage was par with Namibia, lower than Ghana", San Raffaele University microbiology and virology professor Roberto Burioni told CNN past year.
In Bologna, officials said the 300 children did not present the official document attesting to their vaccination on Monday, and so could not attend public nursery schools.
What's next for Brexit after PM May's latest defeat?
May's warning in a tweet, saying: "Today is our Hotel California moment". "In politics, sometimes you get a second chance. In his legal advice on the revised deal, Cox said the risk of this has been reduced, but not eliminated.
Health Minister Giulia Grillo said the rules were now simple: "No vaccine, no school".
The required vaccinations are polio, diphtheria, tetanus, hepatitis B, pertussis, measles, rubella, mumps, chicken pox and Haemophilus influenzae type B.
Parents are now facing fines if their unvaccinated children attend school.
Regional authorities are taking care of the situation through different ways, report Italian media.
In 2017 former Italian health minister Beatrice Lorenzin introduced a policy to obligate children to undergo 10 compulsory vaccinations, a survey found between a quarter and half of the population opposed the new scheme.
Across the world, health authorities are grappling with a global resurgence of measles, with record numbers recorded in Europe and deadly outbreaks in the Philippines and Madagascar. It threatened to overturn the mandatory vaccination law passed by the previous government but ended up scrapping its plans in the face of criticism as the country experienced a measles outbreak last summer.
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