A statement from the Caribbean island nation says that the two women, who were both in their 80s, died from natural causes while on vacation there on Nov. 29.
The government says both bodies were sent to the same funeral home and flown to the U.S. on the same airline and the body of the Canadian woman was then flown to Canada.
The Canadian woman's identity has not been released, but the daughter of the woman from New Jersey says she believes her mother's body was sent to Ottawa by mistake and cremated.
St. Maarten says in its statement that the health inspector will investigate, including ordering a DNA analysis on both sets of remains.
In Canada, a Foreign Affairs spokeswoman says the department has been in touch both with officials in St. Maarten and relatives of the Canadian.
Lisa Kondvar, of Warwick, R.I., has said that her family found another woman's body in her mother Margaret Porkka's casket ahead of her funeral last month.
The two dead women bore no resemblance to one another and were of different frames and heights, she said. The family has hired a detective and is looking for an international attorney.
Emerald Funeral Home director Orlando Vanterpool has said he took the bodies to the airport on the same day and the air trays containing the bodies were identical.
"To my knowledge, we sent the correct human remains," he said. "Everything was regulated with the government. All the paperwork was in order, but apparently somewhere, somehow, something happened."