Tornatore, 51, was taken to a hospital in the Italian capital after two young men attacked him Tuesday evening, the daily newspaper Corriere della Sera quoted the director as saying.
He suffered head trauma as well as several minor injuries, the news agency ANSA reported.
Tornatore was taking a stroll after leaving his office when the two men asked him for directions. While one thanked the filmmaker for the help, the other hit him on the head from behind, Corriere della Sera said.
After that "I don't remember anything," he said. The two men made off with Tornatore's wallet, mobile phone and watch, the paper reported.
The Sicilian-born director, whose "Cinema Paradiso" won the Academy Award for best foreign film in 1990, underwent a CT scan after being hospitalized and was scheduled to have another scan on Thursday, ANSA reported.
Police and hospital officials declined to comment.