According to local authorities, the blaze started on Saturday morning near a furniture store on the third floor of the building.
The cause of the fire remains unknown, the New York Times said.
The fire started as locals were completing their Christmas shopping, and workers inside the building were wrapping up their work before the holiday.
Officials said many of the people trapped inside worked at a call center located in the mall.
"We are currently coordinating with the authorities," said Thea Septaan Padua, a spokeswoman for the mall.
No deaths have been reported so far.
The building has remained on fire and was too dangerous to enter even after more than 24 hours, according to the mall spokesperson.
Firefighters were already there at the spot and struggled to enter the building and rescue the trapped people inside.
Paolo Duterte, Davao's city mayor and the son of incumbent President Rodrigo Duterte said: "Their chances of survival is zero. Our firemen are still struggling to find a way in as the fire is still burning. They are giving their best."
President Duterte made an unannounced visit to the mall on Saturday night and met with the family members of the affected victims.
He has also assured them that the government would extend help.