Security staff were alerted to the crime by the sound of the chainsaw echoing around the
museum’s palaeontology and called the police.
They found the 20-year-old man in a street near to the Natural History museum in Paris’s Jardin des Plantes with the tusk still in his possession.
The chainsaw was found inside the museum.
The man was in custody on Saturday.
The animal's tusks are not the original ones but were added to the skeleton in the 19th century.
A worldwide ban on the ivory trade has so far failed to stop elephant poaching, which is on the rise, especially in Africa.