Nine women have come forward to say they were attacked while celebrating in Milan's Piazza del Duomo.
The allegations are reminiscent of the New Year's Eve attacks in the German city of Cologne six years ago.
Italian police have used CCTV and amateur footage to identify suspects.
In a statement, they said the young men and boys, aged 15 to 21, who were the targets of Tuesday's raids, had been identified as being allegedly involved in sexual assaults, robbery or aggravating wounding in Milan using footage and witness statements.
Police and prosecutors said they were aware of three attacks during the evening in the northern city's central square and said those who took part were either foreigners or Italians of North-African origin. Investigators believe more than nine young women were attacked and are trying to trace other victims.
In one incident a 19-year-old woman who had gone to celebrate the New Year with a friend was set upon by a pack of youths at around 01:30. While her friend managed to get away, the teenager was attacked for almost a minute before she was given help.
Two young German students were pushed up against barriers and sexually assaulted and a girl was attacked separately in streets close to the piazza.
One of the German women, aged 20, said that during the noise of fireworks and music they were attacked by dozens of people. "I realised they were touching me and we wanted to escape but there were too many of them," she told Ansa news agency.
Her friend fell and suddenly she felt hands groping all over her, she said. Video has emerged of the attack showing the two young women trying to escape.
Although police were on duty, the young German complained they did little to help and did not understand them when they tried to explain what had happened in English.
The accounts in Milan have revived memories of a night of rape, sexual assault and robbery carried out near Cologne Cathedral on 1 January 2016 by some 1,000 people, many of them of North African origin.
Cologne police were also accused of failing to respond to the attacks, which were condemned later by then-Chancellor Angela Merkel as "abominable".