The South African artist said he was at a loss to understand why Rome authorities had not removed graffiti as soon it appeared along the bottom of the 550-metre (1,800-feet)-long mural he created out of the dirt caking an embankment of the famous river.
The work, an idiosyncratic take on the Eternal City's defining moments, was inaugurated in April 2016 and has proved a popular free attraction for visitors to the Italian capital.
But its visual impact has been compromised by the appearance of a steadily-growing amount of graffiti in the spaces between some of the images - most of them 'tags', the personalised signatures of the writer.
"Some graffiti artists do great work. I'm less interested in those who simply leave their initials on the wall," Kentridge told Italian daily La Repubblica.
"I know there are many people in Rome to whom this work is dear... out of respect for them, I hope the city authorities will clean up the graffiti," he said.
The message appeared to have been heard. Deputy mayor Luca Bergamo on Friday ordered a team from the city's refuse department to start erasing the graffiti, denouncing the authors of it as "stupid."
Entitled "Triumphs and Laments", Kentridge's 10-metre (33-feet) tall mural was created by washing the dirt off the wall around the images in a technique known as reverse stencilling.
The artist expects it to gradually disappear as pollution and weeds combine to return the cleaned bits of wall to their previous state, a process that he had envisaged taking four to five years.
The frieze provides a non-chronological depiction of Rome's history from pre-historic times up to the Dolce Vita era of the 1960s and the contemporary migrant crisis - which is referenced in a depiction of a Roman slave galley.
In an interview with AFP last year, Kentridge described it as a meditation on the flawed nature of memory with both heroic and shameful episodes from the city's history on show.
The mural is located on the right bank of the Tiber in the Trastevere district of Rome, close to St Peter's basilica and across the water from the historic centre of the Italian capital.