Utrecht police said her body was discovered by friends yesterday evening. Forensic investigators, after working through the night, have ruled out a natural cause of death.
Police expect an autopsy to show whether her death was the result of "an accident or possibly a crime," they said in a statement this morning.
She was seen in good spirits as recently as Saturday, at a function of her centrist D66 political party.
Borst was a medical academic who served as health minister from 1994 to 2002.
Also Read
"She won people over with her openness, mildness and honesty," he said.
Borst's viewpoints were often at odds with those of religious groups, but enjoyed the approval of most Dutch voters.
Trying to prevent a measles epidemic in the Dutch Calvinist bible belt last year, she wrote an opinion piece in newspaper Algemeen Dagblad asking pastors and churchgoers to get vaccinated.
In an interview with newspaper NRC in 2001 she acknowledged she was not opposed in principle to a suicide pill for "very aged people who are finished with life."
But "we have to have a thorough societal discussion of this subject," she told the paper.
Borst, one of the first Dutchwomen to reach high political office, held the title of "minister of state" one of a handful of former leaders given diplomatic passports who are allowed to represent the country on the international stage.