The driver, an Italian of Moroccan heritage, hit several people before crashing into a shop window, colliding head-on with a woman.
Eight people were wounded in the incident in Modena, four of them seriously, including a woman who had to have both legs amputated.
Meloni cancelled a planned visit to Cyprus to go to Modena, a government source said.
Italian President Sergio Mattarella will also travel to the northern Italian city, the source said.
Security camera footage broadcast by Italian media showed a car being driven at high speed into a city centre street packed with pedestrians and cyclists.
The suspect tried to flee the scene but was chased and cornered by four passers-by, then pulled a knife and injured one of them.
The driver, an economics graduate born in 1995 who was not known to the police, went through a spell of “psychological disturbance” in 2022, city prefect Fabrizia Triolo said at a news conference on Saturday.
“He had been treated at a mental health centre for schizoid disorders, but we lost track of him after that initial period of observation in a care facility,” she added.
According to the prefect, the driver was not under the influence of “psychotropic substances”.
His home near Modena has been searched.
Pedestrians tackled suspect
The head of the Emilia-Romagna region, Michele de Pascale, told the news conference on Saturday it was an “extremely serious act, but it is important to understand its nature and motive — let us wait for more information”.
Meloni wrote on X that the incident was “extremely serious”.
“I would also like to express my thanks to the citizens who courageously intervened to detain the perpetrator, as well as to the law enforcement officers for their response,” she added.
His head bleeding, Luca Signorelli, one of the passers-by who intervened, told Italian TV channels that he “heard impacts and saw people being run over.
“The car came at me and I managed to throw myself to the ground,” Signorelli added.
“The car was smoking, I opened the door, and he got away; four or five of us ran after him … He pulled out a knife, hit me in the head, and gave another blow to my heart that I managed to avoid.”
Modena mayor Massimo Mezzetti thanked “those citizens who showed courage and civic duty”.
He added: “We need to understand what’s behind this act. But it was a dramatic event.
“I am deeply shaken.”