Video footage shows a torrent of muddy water and debris streaming down a hilly street in the northern La Gasca district, sweeping away cars and motorcycles.
At least 15 people were injured, the officials say. There are fears that the death toll will rise, BBC reported.
The flooding was triggered by heavy rain in the capital on Monday.
"I saw how the current took a man and a child. It was horrible," local resident Belén Bermeo was quoted as saying by Ecuador's El Universo newspaper.
Local emergency services earlier reported three fatalities. The services also published a dramatic video showing the devastation caused by the flooding.
MP/PR