An autopsy confirmed the 38-year-old Frenchman lost a leg in the rare attack off the coast.
The victim suffered multiple shark bites as she was mutilated while swimming about 500 meters from shore on Thursday.
The young woman, who has not been named, was on sabbatical in the Caribbean when she was attacked.
The secretary general of the prefecture, Mikael Doré, said: “It was probably a large tiger shark, three to four meters long”.
Saint Martin – or Sint Maarten – is divided into Dutch and French territories.
Reports say the attack took place in the waters of the popular Orient Bay, in the northeastern part of the island, in the Dutch section.
Following the incident, local authorities banned swimming and water sports in the area until December 16.
Mr Dore said: “Swimming should be avoided after heavy rains or when the water is cloudy. The shark’s vision is blurry and this can confuse prey. ”
Nicolas Maslach, director of the Saint Martin nature reserve, said: “The time of the attack is very important, but we know that the water was and still is very cloudy. ”
Authorities said they were awaiting confirmation of the daily presence of sharks in local waters before deciding what action to take, according to French news source 20 Minutes.
A scientific watch group has been set up and will meet on Monday.
Experts from Tahiti, Reunion, the United States and the Caribbean shark network will advise you on the next steps to protect the population.
Shark attacks are extremely rare in the Caribbean region, with four fatal incidents among 34 unprovoked shark attacks since 2000.
An unprovoked non-fatal attack in Saint-Martin was recorded in 2005.