The egg was given to the museum's curator Dr Marjorie Courtenay-Latimer in 1915 by her great aunt Lavinia.
She in turn was given it by a family friend who worked as a sea captain and made regular trips to the dodo's native home of Mauritius where he said he found the egg in a swamp.
Together with a pre-historic coelacanth previously thought to be extinct but found in East London Bay and positively identified by Dr Courtenay-Latimer in 1938, the egg draws thousands of visitors a year from all over the world.
Now, the museum's curator has decided to test the veracity of its most prized artefact.
Mcebisi Magadla said the test would involve breaking off a piece of egg the size of a pen nib from the outside of a hole the size of a five pence piece in its surface.
He said it could be tested at the University of Cape Town or further afield in Oxford, where the university's Natural History Museum houses the foot and head of a dodo.
"We have a duty to test the egg to prove its authenticity one way or another and the best way to do that is by DNA testing," he said. "As a museum we cannot say something is authentic unless we can check."
The flightless dodo became extinct in the mid 17th century after being extensively hunted by visiting sailors and the dogs and cats they brought on voyages with them which plundered the birds’ nests.