"Of the 31 suspects whose names are known, 18 have asylum seeker status," said ministry spokesman Tobias Plate, citing federal police figures and indicating that their alleged offences were "mostly theft and causing bodily harm".
Federal police had recorded several complaints about sexual offences, but "the perpetrators for these have not been identified," he said.
The suspects include nine Algerians, eight Moroccans, four Syrians, five Iranians, one each from Iraq, Serbia and the United States, and two Germans, he said.
Victims blamed men of "Arab or North African" appearance, inflaming a heated public debate about Germany's ability to integrate the nearly 1.1 million asylum seekers the country took in last year.