Investigators have not identified any suspects for the assaults that allegedly took place at the port city's party avenue Reeperbahn.
But victims have described the perpetrators as having "African, Arab, or south European appearance", a police spokesman told AFP.
"It can of course be possible that the perpetrators belong to one group, but at the moment, the descriptions are different," said the spokesman, when asked if a parallel could be drawn to the assaults reported in Cologne, on a far larger scale, where assailants are allegedly of North African origin.
Germany was stunned this week by a rash of assaults during New Year's festivities, with Cologne police recording almost 400 cases that ranged from groping to theft to two reported rapes.
Police have said North African asylum seekers and illegal migrants are the main suspects in the Cologne rampage, inflaming a debate in Germany over whether it could integrate 1.1 million asylum seekers who arrived last year.
Chancellor Angela Merkel on Saturday took a firm line against convicted asylum seekers, saying she backed changes to the law to allow the deportation of all those handed jail time, even if it is only a suspended sentence.