A "closed, small" suitcase "in a very bad condition" was found around 11:30 a.m. local time (10:30 GMT) on the coast of Saint Andre.
Earlier it was reported that plane debris found on Wednesday belongs to the same type of aircraft as missing Malaysia Airlines flight MH370.
The wreckage appears to be the wing flap of a Boeing 777 and was found Wednesday morning off the coast of Reunion Island, roughly 380 miles off Madagascar in the Indian Ocean.
Malaysia is "almost certain" that plane debris found on Reunion Island in the Indian Ocean is from a Boeing 777, the deputy transport minister said on Thursday, heightening the possibility it could be wreckage from missing Flight MH370.
However, experts say that the found piece of debris could have come from a twin-engine plane that crashed off the island in 2006, the Malaysia Airlines Boeing that went missing last year, or a Yemeni A310, which fell from the sky off Comoro Islands in 2009.
Flight MH370 went missing en route from Kuala Lumpur to Beijing, disappearing from radar screens on March 8, 2014. The plane was carrying 227 passengers and 12 crew members.