The one-metre-high glass and steel barrier around the famous monument would stop tourists from sitting on or swimming in it, according to the council motion approved last Friday.
But experts have criticised the plan, arguing that it would ruin the view of the landmark.
“Installing a barrier seems a frightful offence against the beauty of a masterpiece which gives itself generously to those who observe it," architect and historian Paolo Portoghesi told Italian media.
He called the plan “truly foolish”, and said it would be enough to have police on patrol at the tourist hotspot.
“If they are not used for specific dangers, gates are follies that destroy the sense of the city,” he added.
“Rome has always sought a direct relationship with those who live there and those who visit it.”
Rome’s former archaeological superintendent Adriano La Regina echoed Portoghesi’s concern.
“As far as the Trevi Fountain is concerned, you have to see it,” he said.
“If tourists aren’t standing or sitting in an unseemly way, and do not get in the way of visiting the fountain, why drive them away?”
Rome Mayor Virginia Raggi has defended the project, saying the barrier would not impede the view of the fountain or affect the tradition of tossing coins into its waters.
Raggi said the barrier would be similar to those already in place around certain Roman fountains such as the Turtle Fountain in Piazza Mattei, or the Fountain of the Four Rivers by Bernini in Piazza Navona.
Describing the plan as “common sense”, Raggi said the barrier would allow police to concentrate on curbing illegal trading in the surrounding piazza.
Rome recently banned tourists from sitting on fountains around the city, but police haven’t always been successful in enforcing the new regulations.
Tourists have also specifically been warned against swimming in the fountains, and anyone caught doing so could face a fine of up to €450.
Despite the pricey punishment, many people still climb on the Trevi Fountain, wash their feet in it, or take a dip in it in hot weather, with some attempting to recreate the famous scene between Marcello Mastroianni and Anita Ekberg in Federico Fellini’s classic film La Dolce Vita.