Highgate Cemetery tweeted that it looks like it was repeatedly hit with a hammer.
Trust chief executive Ian Dungavell said the attack on the Grade I-listed monument, which puts it on a par with the most important buildings in the country, was “deliberate and sustained.”
He added: “It will never be the same again, and will bear those battle scars for the future.
“It’s already scarred with traces of paint and previous damage. I’m really cross about it because it’s a particularly inarticulate form of protest and it’s not going to win any fans.
“Over the years all sorts of things have happened to it, there was even a bomb left close to the memorial, but to be honest this looks like it could be harder to repair, because it’s damage to the marble.”
The marble plaque was first used on the grave of Marx’s wife Jenny von Westphalen in 1881 and shows the dates of the births and deaths of Marx, von Westphalen, their daughter Eleanor, grandson Harry Longuet and of their housekeeper Helene Demuth.
It was moved, along with the remains of Marx and von Westphalen, to a more prominent location in the cemetery in 1954 after the original grave was “not felt to be a suitable marker for someone of such international significance.”
Highgate Cemetery tweeted: “It’s a Grade I-listed monument; this is no way to treat our heritage. We will repair as far as possible.”
The monument is owned by the Marx Grave Trust, represented by the Marx Memorial Library, which will make any decisions about future repairs.
Communist Party general secretary Robert Griffiths told the Star: “The ideas of Marx – like his plinth at Highgate – are powerful enough to outlast any damage done by a fascist vandal.
“This moronic attack should help ensure an even bigger turnout for the annual Marx Oration and ceremony there on Sunday March 17.
“The labour movement and the left in Britain, and internationally, must now ensure that the monument is fully restored as quickly as possible.”