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.

Zimbabwe's nine-wicket defeat by Group A winners India on Monday ensured Ireland's place in the top three.
The Irish lost to India and hosts Sri Lanka but beat Zimbabwe and Thailand.
Ireland retain their one-day international status by making the Super Six, from which the top four qualify for the World Cup this summer.
Sri Lanka finished second in the group while tournament favourites India boasted a 100% record from their four games.
Ireland are are also joined in the Super Sixes by South Africa, Pakistan and Bangladesh.
Their next game is on Wednesday when they face Bangladesh, before taking on Pakistan on Friday and South Africa two days later.
Zimbabwe required a victory over India in Colombo, along with a significant improvement to their net run rate, to overtake Ireland and make the last six.
Ireland completed their group matches on Saturday with a 46-run win against Thailand, who ended bottom of the group.
Kim Garth hit an impressive 98 and Laura Delany added 50 while seamer Lucy O'Reilly took 3-28.
All matches played in Colombo & start at 04:30 GMT. CCC = Colombo Cricket Club; MCA = Mercantile Cricket Association Ground; NCC = Nondescripts Cricket Club; PSS = P Sara Oval

Cardiff University is currently exhibiting some of its collection as part of a three-day event to mark the centenary of Thomas' untimely death.
But Alan Hughes, head of special collections and archive, said some other items were in poor condition.
The National Manuscripts Conservation Trust has awarded them almost Â£3,000.
The university holds the largest archive of Thomas' letters, diaries, notebooks, poems, photographs and personal belongings.
Mr Hughes said the grant had allowed us it to "collaborate with Glamorgan Archives to undertake essential conservation work on many of Edward Thomas' notebooks".
He said nine were in particularly poor condition due to acidification, fragile bindings and general deterioration over time.
"Many are unable to be handled without a high risk of further damage and are therefore inaccessible to scrutiny, celebration, digitisation and study," he said.
Thomas, known for his poems written as World War One raged across Europe, was killed in the Battle of Arras at Easter 1917, at the age of 39.
While he was born in England, Prof Katie Gramich who organised this week's event, said his parents were Welsh and he loved Wales.
She said his work was influenced by the time he spent walking in Wales and he felt "cheated of a Welsh identity".
The exhibition, which runs until the autumn, features previously unheard archive recordings of family and friends, interviewed by the university's Prof R George Thomas in 1967.
Italian police say four teenagers accused of 12 robberies in Milan gloried in violence like the notorious gang in the film A Clockwork Orange.
[NEXT_CONCEPT]
Ireland have progressed to the Super Six stage of the Women's World Cup Qualifier after finishing third in their group in Sri Lanka.
[NEXT_CONCEPT]
A collection of manuscripts and notebooks which belonged to poet and novelist Edward Thomas are to be conserved thanks to a grant.