The by-law, the first such measure to be introduced in Italy, was voted by the city council Friday, according to the municipal website, quoting mayor Letizia Moratti as saying it was necessary to protect young people.
The website said that a third of children as young as 11 had already experienced alcohol problems in Italy's second city.
According to national health authorities, one-sixth of hospital admissions for alcohol abuse concern youngsters under 14.
The by-law will come into effect on Monday for a trial period of 120 days in Milan, and will be enforced by local police.
The fine, which will be increased to 500 euros if not paid within five days, will also apply to suppliers of alcohol to children.
Italian law generally only has a ban on the sale of alcohol to under-16s in cafes, bars and discos, though some towns have extended it to shops.