The first attack on Feb. 4 had caused damage on the marble, which was taken from the original 1880 grave and was moved to a prominent spot in 1956.
German philosopher Marx moved to London in 1849 and lived in the British capital for the rest of his life in exile.
He died on March 14, 1883, when he was 64-years-old.
“It’s battle-scarred and has all the marks of a rich and varied life,” Ian Dungavell, chief executive of the Friends of Highgate Cemetery Trust had said following the first attack
“It’s not irreparable but it will never be the same again,” he had added.
The tomb is a Grade I-listed monument, meaning it is under protection as a heritage asset.
Marx is known as the father of communism ideology and known with his Communist Manifesto and Das Kapital (Capital).