Thousands of people protested against the railway's construction on Saturday in Piedmont's Susa Valley, near the French border.
The project, which aims to reduce road and air travel in the Alpine region by cutting travel times, has been met with opposition since its launch over 30 years ago.
During the protest, several hundred people attacked the police who were protecting the construction site, according to Italian authorities.
Videos published by Italian media showed black-clad protestors with their faces covered hurling petrol bombs and projectiles in the direction of police.
Meloni, who visited the site on Monday alongside Interior Minister Matteo Piantedosi, said more than 120 officers had been injured.
"This is organised, premeditated violence and must be treated as such, and we will do everything we can to bring these individuals to justice," Meloni said.
Four people were been arrested, Italian news agency ANSA reported.
Franco-Italian company Telt said that a preliminary investigation showed that the resulting damage from the protest at Chiomonte, west of Turin, reached about one million euros.
It did not specify whether the damage would substantially delay the ongoing project.
"The time required to clear the rubble and restore the workspaces and services in the gallery has yet to be assessed,” said Telt, adding that around ten workers who were at the site on Saturday "were immediately evacuated and brought to safety".
A large proportion of the protesters were so-called Black Bloc hardcore demonstrators from France, as reported by several local media outlets.
Contacted by AFP, Italian police did not provide further details.
Interior Minister Matteo Piantedosi said on Saturday, however, that three French nationals travelling to the site had been turned back, after masks, fireworks and an angle grinder were discovered in their vehicle.
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