The area was sealed off to visitors at the time and the discovery was made by staff at the ancient site.
The Garden of Severus is already part of the Great Pompeii Project, a multi-million euro fund from the EU and Italian government to protect the area.
An agreement is also being set up with the fire service to intervene in inaccessible parts of Pompeii which are at risk, the superintendency said.
The incident at the Garden of Severus is just the latest in a series of collapses at Pompeii, which was destroyed by a volcanic eruption in 79AD.
Culture Minister Dario Franceschini last March promised to unblock €2 million in restoration funds , after the Temple of Venus and Pompeii walls were damaged by rainfall.
Despite the site winning funding to the tune of €105 million, the Italian authorities have been criticized for being woefully slow in implementing restoration plans.
Unesco has also weighed into the debate, threatening in 2013 to scrap Pompeii from its prestigious World Heritage list if measures were not taken to save the ancient site.