Police arrested a 30-year-old Vancouver man at the scene of the incident on Saturday evening, describing him as having had a "significant history" of interactions with authorities involving mental health.
They said there was no evidence of terrorism.
"This is the darkest day in our city's history," Vancouver Interim Chief Constable Steve Rai told reporters at a Sunday press conference.
He said dozens of people were injured, some seriously, and warned that the death toll could rise in coming days and weeks.
The attack on Saturday evening took place two days before Canada's federal election on Monday.
Canadian Prime Minister Mark Carney's campaign movements were delayed on Sunday morning but he resumed campaigning after making a statement in which he expressed his condolences to the country's Filipino community.
"Last night, families lost a sister, a brother, a mother, a father, a son or a daughter. Those families are living every family's nightmare," he told reporters in Hamilton, Ontario.
"I join all Canadians in mourning with you. I know that Canadians are united with you," he said.
More than 12 hours after the incident, police still did not have a motive for the attack at the festival, which took place without a dedicated police presence or heavy vehicle barriers.
"There were no known threats to the event or to the Filipino community," said Rai, noting that more than 100 police officers have now been assigned to the case.
The suspect was initially chased down and held by festival-goers until police arrived, witnesses said.
The injured were taken to multiple hospitals, police said.
The incident happened shortly after 8pm in Vancouver's Sunset neighbourhood, an area known for its large Asian population, where the Lapu-Lapu Day Block Party, celebrating a Philippine hero, was taking place.
One witness told CTV News he saw a black vehicle driving erratically in the area of the festival just before the crowd was struck.
A photo of the aftermath posted online showed a dark Audi SUV with both front fenders crumpled and the hood pushed up toward the vehicle's windshield.
Philippines President Ferdinand Marcos Jr said he was "shattered to hear about the terrible incident" and extended his "deepest sympathies to the families of the victims and to the strong and thriving Filipino community in Canada".
"The lives lost will not be forgotten," he said in a statement.
Local authorities set up a 24-hour assistance centre at a nearby park facility to help anyone who had not been able to contact a loved one at the festival.
Online images showed the bodies of victims on the pavement alongside a row of colourful food trucks as others attended to them on a roadway littered with debris including what appeared to be a motorised scooter.
The festival - celebrated especially in the central Philippines - honours Datu Lapu-Lapu, a Filipino chieftain who defeated Spanish forces led by Ferdinand Magellan in the Battle of Mactan in 1521.
The government of British Columbia officially recognised April 27 as Lapu-Lapu Day in 2023, acknowledging the cultural contributions of the Filipino-Canadian community, one of the largest immigrant groups in the province.
King Charles, Canada's head of state, said in a statement: "Both my wife and I were profoundly saddened to learn of the dreadful attack and utterly tragic loss of life in Vancouver, which took place as the Filipino community came together to mark the celebration of one of their most special festivals."
The centrepiece of the festival in Vancouver is a multi-block street party featuring Filipino food and traditions, live performances and cultural displays.
"I didn't get to see the driver, all I heard was an engine rev," Yoseb Vardeh, co-owner of food truck Bao Buns, said in an interview with Postmedia.
