The blast tore through a street market outside the high-end Marco Polo hotel, a frequent haunt of Duterte, who was in the southern city of Davao at the time but was not hurt.
"We were having a meeting and we heard a very huge explosion. The first thing we thought was 'it's a bomb'," said John Rhyl Sialmo III, 20, a student at the nearby Ateneo de Davao University.
"The area where there was the explosion was a massage parlor. So we saw these men and women from that place in their uniform, they went to the school lobby to seek help. They were soaked in blood."
Presidential spokesman Ernesto Abella, speaking to CNN Philippines, described the blast as an "unspecified explosion".
"There is nothing definite about it but it has resulted in the death of ... at least 10 persons, and injury of about 60," Abella said. Police later said two of at least 30 people taken to hospital had since died, bringing the toll to 12.
Regional police chief Manuel Guerlan said a ring of checkpoints had been thrown around the city's exit points.
"A thorough investigation is being conducted to determine the cause of the explosion," he said. "We call on all the people to be vigilant at all times."
Duterte is hugely popular in Davao, having served as its mayor for more than 22 years before his stunning national election win in May, garnered from the popularity of a promised war on drugs.
His election has prompted a spike in drug-related killings, with more than 2,000 people killed since he took office on June 30, nearly half of them in police operations.
Duterte has typically spent his weekends in Davao, in the far south of the archipelago nation, since taking office, so his presence there on a Friday was not unusual and he had given a televised news conference earlier in the day.
His son Paolo Duterte, who is vice mayor of the city, told Reuters that his father was nowhere near the scene of the blast, which happened around 10:30 p.m. (1030 a.m. ET), and afterwards was safe at a police station.
Five men and five women were killed, Paolo Duterte said. There was no immediate claim of responsibility.
"It's a sad day for Davao and a sad day for the Philippines," Paulo Duterte said later in a statement.
Davao is located in Mindanao, a large southern island beset by decades of Muslim insurgency. The region is also home to Abu Sayyaf, a rebel group loosely linked to Islamic State and notorious for making tens of millions of dollars from kidnappings.
However, Davao itself is largely peaceful and Duterte has been credited with transforming it from a lawless town to a southern commercial hub for call centers and offshore business processing services.
Duterte had earlier on Friday shrugged off rumors of a plot to assassinate him, saying such threats were to be expected.
Asked on Thursday about the same rumor, presidential spokesman Abella described Duterte as heroic and said: "He eats that for breakfast, it’s not something new to him."