The blast occurred just before 11.00 PM (local time), leaving bodies strewn amid the wreckage of plastic tables and chairs on a road that had been closed to traffic for the market in the heart of Davao city.
An improvised explosive device caused the explosion, presidential spokesman Martin Andanar said, adding drug traffickers opposed to Duterte's war on crime or Islamic militants may have been responsible.
"There are many elements who are angry at our president and our government," Andanar told DZMM radio, after referring to the drug traffickers and the militants.
Ten people were confirmed killed and up to 60 others injured, according to city police spokeswoman Catherine dela Rey.
More From This Section
Davao is the biggest city in the southern Philippines, with a population of about two million people. It is about 1,500 kilometres from the capital of Manila.
The blast occurred in the centre of Davao, close to one of the city's top hotels and a major university.
"The force just hurled me. I practically flew in the air," Adrian Abilanosa, who said his cousin was among those killed, told AFP shortly afterwards.
Communist rebels, who have been waging an armed struggle since 1968, also maintain a presence in rural areas neighbouring Davao.
Duterte had been mayor of Davao for most of the past two decades, before winning national elections in a landslide this year and being sworn in as president on June 30.
Duterte became well known for bringing relative peace and order to Davao with hardline security policies, while also brokering local deals with Muslim and communist rebels.
As president, Duterte quickly launched peace talks with the communists, who last week agreed to an indefinite ceasefire.
Duterte has also in recent weeks pursued peace talks with the two main Muslim rebel groups. Its leaders have said they want to broker a lasting peace.