The four are now in police custody, after a crime spree that included raids on hotels, small shops and amusement arcades, Italian media report.
On one occasion they allegedly raced off in a Porsche Cayenne after pointing a pistol in the driver's face.
The gang reportedly boasted of their crimes in video clips on social media.
They stole cash, smartphones, tablets and even on one occasion a youth's luxury shoes worth â‚¬530 (Â£465; $601), according to police. The crimes took place in Milan's Quarto Oggiaro district.
Two of the young suspects are Italians aged 14 and 16, the others are of foreign origin, aged 15 and 17.
They came from broken homes and are thought to have been controlled by an Egyptian man, aged 23. He is under arrest on a drugs charge and was convicted for previous offences.
Police found that the youths - dubbed a "baby gang" in Italian media - possessed several firearms, including a pump-action shotgun.
Italy's Rai news website said investigators "stressed that the baby gang used brutal violence on their victims in the style of A Clockwork Orange".
One victim, a young man attacked in the street, was pistol-whipped and needed 10 stitches for a deep wound.
The 1971 film A Clockwork Orange, directed by Stanley Kubrick, was a box-office hit. Based on a futuristic novel by Anthony Burgess, it portrayed a gang of juvenile delinquents who made a cult of gratuitous violence.
Italian police say four teenagers accused of 12 robberies in Milan gloried in violence like the notorious gang in the film A Clockwork Orange.