The claim was triggered by a photograph and video circulated on social media which showed one of the masked youths who smashed shop fronts and torched cars in protests against Expo 2015 apparently sporting a Rolex-style wrist piece.
In an open letter published in the form of adverts in Italian newspapers on Wednesday, Rolex's Italian boss Gianpaolo Marini demanded an apology from Renzi and interior minister Angelino Alfano.
"I have to express my profound regret and disappointment over your comments and their implicit association of window-breakers and the fact of wearing a Rolex watch on your wrist," Marini wrote.
He said there was no way it could be established that the vandal photographed had been wearing an authentic Rolex.
"Unfortunately your words had a huge echo and produced an unacceptable juxtaposition of the image of Rolex with the devastation of Milan and the world of subversive violence," Marini said.
It was the second time in a couple of months that Rolex has been in the news in Italy.
Former transport and infrastructure minister Maurizio Lupi was forced to resign over a scandal which partly centred on allegations his son had been given a Rolex as a gift by a businessman suspected of benefiting from corruption in public works tenders.
Rolex did not comment on that occasion.