Pravind Jugnauth’s office said the damaged MV Wakashio’s hull, which struck a reef near the island last month, will crack and “eventually” break.
But he said the situation was “very serious” as the bulk carrier still has 2,000 tonnes of oil on board its two tanks in good condition and ministers are preparing for a “worst-case scenario”.
In a televised speech, Mr Jugnauth said: “The rescue team observed several cracks in the hull of the ship, which means that we are facing a very serious situation.
“We have to prepare for the worst-case scenario. It is clear that at some point the ship will collapse. ”
At least 1,000 tonnes of oil are estimated to have entered the waters of the Indian Ocean, which environmental group Greenpeace says could be a major ecological crisis.
Locals have worked to prevent it from ruining the waters, coral reefs and beaches that support the island’s main fishing and tourism industries.
A massive clean-up operation is underway consisting of making floating dams from leaves and human hair.
But it may already be too late, as environmentalists have said they are starting to find dead fish as well as oil-covered seabirds.
The Mauritian government has declared a environmental emergency, pleading for international aid, and France – its former colonial ruler – sent aid.
The MV Wakashio, owned by the Nagashiki Shipping Company and operated by Mitsui OSK Line, reportedly carried 4,000 tonnes of fuel oil when it ran aground on July 25.
The operator is committed to “All in his power” to help alleviate the disaster after fuel began to leak from the cracked ship on Thursday.
Last year, tourism contributed 63 billion Mauritian rupees (£ 1.2 billion) to the economy of the country, which has a population of around 1.3 million.