Eleven women, from Tyrol, Vorarlberg, Italy, Germany and Switzerland, told police that they were harassed and groped by a group of men in and around Innsbruck's Marktplatz, where public Silvester celebrations were taking place.
A police spokesman told the ORF broadcaster that the allegations are being investigated, and that police are waiting to view video and mobile phone footage from that night - some of which was filmed by the organisers of the event.
The women all said that they were assaulted by a group of dark-haired men who appeared to be under the age of 30, and that most of them had beards.
Two women who were harassed took photos of two of the men with their mobile phones, however the quality of the photos is not very good as it was already very dark outside. Police said that they questioned all the victims on New Year's Day, before they returned home.
A police spokesman said it's likely that it was one group of men who harassed the various women, and that the men “had a system”. They targeted women who had become separated from their friends or a larger group of people, or were dancing by themselves. Most of the assaults happened between 11.30pm and 1.30am in Marktplatz, when the noise and excitement was at a peak.
A further four women have reported that they were sexually assaulted during New Year's Eve celebrations in the city of Salzburg. A 31-year-old German woman told police that she was harassed by an 18-year-old asylum seeker who appeared to be very drunk and repeatedly tried to kiss her, before grabbing her between the legs.
The woman's friends managed to push him away and he was later arrested and questioned by police, who said that he appeared to be confused and disorientated. He was examined by a doctor and is being held in police custody.
In Graz, a 26-year-old woman told police that she was sexually harassed and assaulted by two men in the centre of the city early on New Year's Day. She said that they grabbed her buttocks and crotch but that she managed to run away and called the police. She said that both men appeared to be foreigners and were between 25 and 35 years old.
Austrian police distributed thousands of rape alarms on New Year's Eve to help prevent incidents like the mass sex assaults in neighbouring Germany a year ago.
Several hundred thousand visitors rang in the New Year in the capital Vienna, which hosted its annual New Year's Eve party trail in the centre, but no incidents or assaults were reported.
In 2015, hundreds of women were mugged and groped in a crowd of men of mainly Arab and north African appearance in the German city of Cologne on December 31. The incidents shocked Germany and fuelled criticism of Chancellor Angela Merkel's liberal refugee policy.