Italy has struggled to absorb thousands of immigrants in recent years, many of them fleeing the civil war in Syria and travelling through North Africa to the Mediterranean island of Lampedusa on flimsy boats.
The issue has become a political battleground. Rights groups have complained about the conditions in centres while the anti-immigration Northern League has said the government is being too generous to new arrivals.
The thirteen, who arrived in October and were taken to the Ponte Galeria centre the following month, sewed their mouths shut on Saturday night, said police.
"They've been left in complete uncertainty, no-one has explained anything to them," said a spokeswoman for LasciateCIEntrare, a protest group set up to highlight the tough conditions in the migrant reception centres.