The 46-year-old owned a luxury spa on the tourist island of Roatan, Honduras, and had lived in the country for over a decade, according to local media.
Police said her partner, Lenin Arana, is being questioned in connection with the case.
"We regret the death of a resident of this island, Mrs. Nedenia Post, who apparently was killed by her partner, Lenin Arana. This person has been detained and has been put before the courts," Roatan police chief Alexis Madrid said.
Madrid said that police are investigating whether Arana was involved and whether or not alcohol or drugs may have been a factor.
"We know this person (referring to Arana) has been, supposedly, a drug user but the forensic and medical studies will be the ones that determine if, in fact, this person had ingested alcohol or some other hallucinogenic that could possibly have led him to commit this atrocious crime," he said.
According to the Washington D.C.'s Hillwood Museum which was the former home of Marjorie Merriweather Post, she was 27-years-old when she inherited Post Cereal Company that became General Foods, Inc. She was a lover and generous donor of the arts. Honduran newspapers say Post Dye did charity work to help youth in the impoverished, Central American nation.
Nedenia Post Dye, a U.S. businesswoman and the great-granddaughter of socialite Marjorie Merriweather Post, was found dead in Honduras and police suspect she may have been killed, authorities said.