The sandstone sculpture of an unnamed infantryman in Glasgow’s Kelvingrove Park was targeted, with the statue’s feet broken off and its face smashed in.
It was erected in 1909 as a tribute to the officers and men of the Highland Light Infantry who died while fighting in South Africa.
The memorial was paid for public subscription, with a plaque explaining it was raised by “comrades and friends”.
Glasgow City Council is now assessing the damage to the statue and how it can be repaired.
A spokesman said: “This is a truly depressing and shameful act of vandalism.
“The statue was originally raised by ordinary, local men in tribute to their fallen comrades and is very much part of the story of Glasgow.
“The roll of honour on the plinth still resonates sharply with families all across the city and they will be aghast at the damage done.
“Whoever is responsible has not only defaced a statue, but also put an ugly scar across a much loved public space.
“If anyone has any information about who was responsible then we urge them to contact the police.”
Police believe the incident took place around 11.30pm on Tuesday, February 12.
The Second Boer War lasted for three years after conflict broke out in 1899 between the British Empire and two Boer states, the South African Republic and the Orange Free State,
More than 300,000 British soliders served in the war, with over 22,000 killed.