Rescue teams searched homes and streets covered by mud following the worst deluge in nearly two decades.
The torrential rains on Monday night caused a build-up of water in a gorge near the working class neighborhoods of La Gasca and La Comuna, sending mud and rocks down on residences and affecting electricity provision.
The country's disaster management agency said 48 people were injured.
"We saw this immense black river that was dragging along everything, we had to climb the walls to escape," said resident Alba Cotacachi, who evacuated her two young daughters from their home. "We are looking for the disappeared."
Footage obtained by Reuters showed a man struggling to free himself from the muddy waters rushing down a residential street. Reuters witnesses said the man was swept away as residents screamed for help.
Other videos showed a torrent sweeping away trees, vehicles, dumpsters and even electricity poles, while some people were rescued from the muddy water by neighbors.
Authorities have not ruled out the possibility of further landslides. The mayor's office has set up shelters for affected families and has started clearing streets in the city.
Ecuador is facing heavy rains in several areas, which have caused rivers to overflow and affected hundreds of homes and roads.
Rains in Quito on Monday were equivalent to 75 liters per square meter, the highest in nearly two decades.