The debris was found on the Mauritius island of Rodrigues by a vacationing couple, news.Com.Au reported citing Reunion island website Clicanoo.
Read more from our special coverage on "MH370"
"The Malaysian government is working with officials from Mauritius to seek to take custody of the debris and arrange for its examination," Australian Transport Minister Darren Chester said.
"This debris is an item of interest however until the debris has been examined by experts it is not possible to ascertain its origin."
However, it remains unclear which country would examine the debris.
Aviation expert Don Thompson told the Australian news website the fragment could be the internal bulkhead from the Malaysia Airlines' Boeing 777 business or economy class cabin.
The latest discovery came less than two weeks after Australian and Malaysian authorities said two pieces of debris found in Mozambique were "almost certainly from MH370".
Another fragment picked up near Mossel Bay, a small town in Western Cape province in South Africa, would also be analysed to see if it came from MH370, South African officials said last month.
Before the latest discoveries, only a wing part recovered from the Indian Ocean island of Reunion, which lies east of Mozambique and neighbours Mauritius, had been confirmed as coming from the jet that disappeared two years ago.
Australia is leading the search for MH370 in the remote Indian Ocean, where the Kuala Lumpur-Beijing flight is believed to have diverted when it disappeared on March 8, 2014 carrying 239 passengers and crew.
Chester added that authorities "remain hopeful the aircraft will be found". More than 95,000 square kilometres (36,700 square miles) of the target zone of 120,000 square kilometres has been scoured so far, but no crash site has been found.
The governments of Australia, China and Malaysia have said they will end the hunt when the target area is fully searched unless new, credible information emerges.
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