Though the fountain has been drained for the renovation, a small basin has been set up at the rim so that visitors can continue the tradition of throwing a coin into the waters with their back turned - a custom which is said to bring good luck.
"The restoration works are invasive and will be disruptive for the thousands of tourists who come every day, but we thought the walkway would be the best way to show off the fountain," Fendi's CEO Pietro Beccari told AFP.
The plexiglass bridge "is a way to show people the fountain from a position no-one has been in before," he said.
While much of the elaborate Baroque facade is now hidden under scaffolding, tourists crossing the basin on the walkway will be able to get a close look at the restoration as it takes place.
The €2.18 million repairs on the nearly 300-year-old fountain will take 18 months, Beccari said.
While some tourists said they were curious to try out the bridge, others complained about finding one of the most iconic monuments in Italy under wraps.
Penny in the fountain
"We were very surprised because we thought we were just going to throw a penny in the fountain. But I'm kind of excited to see what is going on here," said American tourist Pat, while Coco from Hong Kong said he was "really quite disappointed" to find the basin empty of water.
There had been concern about the state of the Trevi Fountain, which is visited by millions of tourists every year, particularly after bits of its elaborate cornice began falling off in 2012 following a particularly harsh winter.
"Patronage is essential in maintaining and restoring our marvellous works of architecture, archaeology and art," Rome Mayor Ignazio Marino said, as he chucked a coin over his shoulder into the temporary basin.
Fendi, founded as a leather goods business in Rome in the 1920s and now part of French luxury giant LVMH, will also be funding the restoration of the Quattro Fontane, late Renaissance fountains which grace each corner of a busy intersection in the capital.
It is not the only fashion house to fund the renovation of the eternal city's monuments: luxury jeweller Bulgari announced earlier this year that it would help clean up the city's famous Spanish Steps, while shoemaker Tod's is financing works at the Colosseum.
Under the deal with Rome city authorities, Fendi's logo can be displayed on building site signs during the repairs and the company can hang a plaque near the monuments for four years after completion.
The Trevi Fountain, commissioned by Pope Clement XII in 1730, is the end point of one of the aqueducts that supplied ancient Rome with water.
It famously featured in a scene of Federico Fellini's iconic film La Dolce Vita in which Marcello Mastroianni and co-star Anita Ekberg share a kiss while wading through its pristine waters.