The blaze, which started around 05:00 local time on Monday (22:00 BST on Sunday), also destroyed 80 homes.
It started on the second floor of a house in a crowded settlement inside the sprawling campus of the University of the Philippines, in Quezon City.
The cause of the blaze is unknown.
Senior fire officer Greg Bichayda told AFP news agency that it took nearly two hours to extinguish the blaze.
“The fire spread quickly,” Mr Bichayda said, adding that victims were unable to escape their homes.
He said six of those who died were children, but no further details of their ages were released.
“The houses consist of light materials. When the fire broke out, people were shocked,” Mr Bichayda said.
“Our station was just nearby but they weren’t able to call us immediately.”
The Philippines is one of the most densely-populated countries in the world, and its capital has a large number of residents per square kilometre.
Metro Manila, the region which comprises the capital and other cities including Quezon, has a population of about 13 million.
Thousands of people live in overcrowded communities where fires are common.