The required vaccinations are polio, diphtheria, tetanus, hepatitis B, pertussis, measles, rubella, mumps, chicken pox and Haemophilus influenzae type B.
The new law came amid a surge in measles cases - but Italian officials say vaccination rates have improved since it was introduced.
Children can not attend nursery schools unless they are vaccinated, and parents of elementary and middle school pupils risk fines of up to 500 euros if they don't have doctor's notes showing that their children were vaccinated against the required diseases.
Cracking down on parents unable to produce the documents, Bologna, the largest city of the Emilia-Romagna Region in Northern Italy, barred more than 300 children failing to present immunization records, from attending school.
The goal of the law, according to a government website, is to fight the gradual decline in Italy's vaccination rates.
"No vaccine, no school", health minister Giulia Grillo said, per the BBC.
China blocks United Nations resolution seeking sanctions on Maulana Masood Azhar
China will continue to communicate and work with relevant parties in a responsible manner so as to properly resolve this matter. All eyes are on China, which has in the past blocked India's bids to get Azhar listed as a UN-designated global terrorist.
Regional authorities are taking care of the situation through different ways, report Italian media.
In other areas there have been no reported cases, while still others have been given a grace period of a few days beyond the deadline.
But up until Tuesday, a temporary measure meant students could remain in school as long as their parents said they were vaccinated. At present, this target is not being achieved (it is now around 80 percent), said health officials. Such a low rate adversely affects herd immunity that prevents the spread of infection.
That includes babies too young to be vaccinated themselves, or those with medical conditions such as a compromised immune system.
The outbreak prompted the government to formulate tough laws.
Fears in the United Kingdom about vaccinations causing autism were recently disproved after the doctor making the claims was struck off the United Kingdom medical register for making the claims in a fraudulent paper which drew from a case study of only 12 children.