Local man Michele Bordoni, 27, injured three people when he crashed a Toyota Yaris in a pedestrian zone in central Sondrio on Saturday afternoon.
“I should have killed more of them,” Bordoni reportedly said as he was arrested.
Prosecutors are preparing to charge him with attempting to “indiscriminately kill a number of people”, as well as assaulting a police officer and resisting arrest, according to papers filed on Monday.
Bordoni, who was initially hospitalized before he was taken to prison on Sunday, is believed to have been under the influence of alcohol and possibly drugs at the time of the attack.
He crashed the car into a pillar near Sondrino's central square before attempting to flee the scene on foot.
One woman was thrown onto an ice rink set up as part of the town's Christmas market. She was taken to hospital in a serious condition but is now said to be out of danger.
Two men were also treated for minor injuries.
It is not clear what motivated the attack. Investigators ruled out terrorism early on, according to La Repubblica.
Last December a Tunisian-born man who had lived in Italy, Anis Amri, drove a truck into a German Christmas market in Berlin, killing 12 people. Four days later, Italian police shot and killed him in Milan.
Another Tunisian man, who was believed to have become close to Amri in prison in Sicily, was subsequently expelled from Italy.