The suspect device was found in the Mazzini square and is being investigated.
Authorities were first alerted to the danger at shortly before 6pm local time.
Italian publication Il Messaggero reports police sources as saying the device was homemade.
It consisted of a cylinder of gunpowder, with shrapnel embedded and electric vires sticking out.
Bomb disposal experts are on scene investigating the incident.
According to Il Messaggero the device was designed so it “could have exploded”.
Adnkronos reports the suspect package was found by a car belonging to Marco Doria, president of park and historic villa redevelopment in Rome.
Mr Doria has received a number of threats since being appointed to his current role two years ago.
Il Messaggero reports he was targeted after finding “many irregularities”.
Describing the campaign of intimidation they quote Mr Doria as stating: “They opened the car and rummaged through my papers, left a .38 caliber bullet with a cross-cut tip in the car.
“They tried to set my house on fire by placing primers here and there in the garden.
“I even found a homemade bug in the car. That’s enough.
“I’m afraid, I haven’t even seen my daughter this summer.”
The Group A match between Italy and Switzerland began at 7.45pm.
Earlier Wales won a sensational 2-0 victory over Turkey in today’s other Group A game.
Aaron Ramsey and Connor Roberts scored in front of 30,000 fans in Baku, most of whom were supporting Turkey.
On Saturday Wales drew 1-1 with Switzerland, meaning they now have a decent chance of making it out of their group.
Italy thrashed Turkey 3-0 in the opening Euro 2020 match.
More to follow…