The fragment was found by two hotel guests staying at the Mourouk Ebony Hotel on the coast of Rodrigues Island, in the Indian Ocean, near Mauritius.
Press reports in Australia have said photographs of the part appeared to match part of an MAS Boeing 777 cabin.
If proven to be from the missing plane, the debris would be the first possible internal fragment to have been found.
Police were in possession of the debris, and Malaysian authorities are expected to lead the investigation.
Mauritius, a volcanic island nation in the Indian Ocean renowned for its beaches and reefs, lies east of Madagascar. A piece of debris thought to be from the missing airliner was found on a sandbar off Mozambique, and another piece recovered from a South African family were believed to be highly likely from the MAS aircraft.
The aircraft, with 239 people on board, went missing while en route from Kuala Lumpur to Beijing on flight MH370. Experts believe it was diverted off course and crashed in the southern Indian Ocean off the Australian west coast.
So far more than 95,000 square kilometres of the 120,000 square kilometre search zone in the Indian Ocean have been completed.
MH370: Another piece of debris found in South Africa
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Mozambique debris ‘almost certainly from MH370′
