The incident occurred shortly after 11pm on Tuesday night, as the woman, who has been named as Tiziana Laudani, was walking close to the Tiburtina train station.
She is thought to have fallen through a metal grate into a disused underground car park.
Two men who had been with Laudani were also injured and in a state of shock after apparently trying to save their friend.
Firefighters were still working to establish the exact cause of the accident on Wednesday morning, as well as how the three people entered the area. According to Il Messaggero, the two men told police they had gone into the square to get a better view of some shooting stars.
The square has been closed to traffic for seven years; in 2009, works began on building an underground car park, but the contractors responsible went bust, and the area has been left to fall into disrepair.
Protesters have complained about the danger of the area on several occasions.
"It breaks our hearts that our many efforts were not enough to get the area's most important square redeveloped so that this tragedy could be avoided," said one local activist Fabrizio Montanini, according to La Repubblica.