"Five vehicles are on the scene at the moment and 21 firefighters, assisted by Table Mountain National Parks," he said.
"The fire is fanned by south-easterly winds and has not been contained yet."
The cause of the fire was undetermined.
The Rhodes Memorial is a statue of English-born South African politician Cecil John Rhodes designed by Sir Herbert Baker. The statue sits at the foot of Devil's Peak.
A statue of Rhodes at the University of Cape Town has been at the centre of controversy.
Students have been protesting over the statue saying represents institutionalised racism at the university.
Last month, protesters threw human excrement at the statue.
On Friday, UCT Vice Chancellor Dr Max Price reportedly called on students to participate in the process surrounding the proposed removal of the statue present on the campus.
On April 8, UCT's council is expected to have a special sitting to vote on the removal of the statue.
If passed, Heritage Western Cape will need to approve it.
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