Tempers flared after a 19-year-old woman from the Netherlands and a 44-year-old Italian-American woman wanted to take selfies at a prime spot in front of the monument at the same time.
A bitter verbal exchange soon spilled over into physical aggression and a full-scale brawl when family members from both side entered the fray.
Startled onlookers said at least eight people ended up scrapping in front of the world famous tourist attraction.
Two police officers managed to restore order for a few minutes but reinforcement had to be called when hostilities resumed.
The tourists sustained bruises but have not been charged over the violence.
News of the “selfie spat” arrives just days after a Roman city councilor revealed officials were considering barring tourists from lingering at the monument to combat the fountain’s serious overcrowding, floating the idea of creating a route to pass it by.
Andrea Coia said said: “We’re looking at the idea of having a route which would allow tourists to see the Trevi Fountain but without stopping.”
The Trevi fountain, designed by the architect Nicola Salvi and completed by Giuseppe Pannini in 1762, attracts thousands of visitors each year.
Patrols at the site were increased after a £1.4m facelift in 2015.
Earlier this year two Scottish rugby fans were fined £400 each for taking a swim in the fountain.
Officers pulled the men from the waters and cordoned off access to the fountain until 1am to prevent other «tipsy» fans from taking a swim.
The men were «cheered on» by a crowd of fellow fans on St Patrick’s Day, after the Scotland rugby team triumphed 29-27 against Italy in the Six Nations.
The files came after Rome pledged to crack down on bad behaviour at the fountain, imposing fines on people caught snacking or camping on the fountains’ pedestals, dipping their feet in the water or going for a swim.
The authorities get particularly hot under the collar when tourists try to recreate the scene from Federico Fellini’s film La Dolce Vita, in which the late Swedish actor Anita Ekberg wades into the fountain.