Major Harin Gonzaga, 37, was found by his wife with a gunshot wound to the heart inside his room in the Malacanang compound in Manila, said Brigadier General Lope Dagoy, head of the Presidential Security Group.
Dagoy said there were no initial signs of foul play or any indication of a struggle but police were still investigating.
The incident took place far from Duterte's residence inside the compound, Dagoy said, adding that even other members of the security force were unaware of the shooting until Gonzaga's wife found the body.
The wife, who is a sergeant in the security force, said the couple were not facing any problems apart from Gonzaga's heavy workload, Dagoy told reporters.
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Gonzaga was in charge of the security force's operations and was not one of the president's personal guards, he added.
Duterte was elected in a landslide last year on a vow to eradicate illegal drugs in society by killing up to 100,000 traffickers and addicts.
Since he assumed office 15 months ago police have reported killing more than 3,800 people in anti-drug operations, with many more killed in mysterious circumstances.
Despite criticism from human rights groups, he still enjoys widespread support among Filipinos who see him as a charismatic anti-establishment politician and their best hope of reducing crime and corruption.
