Witnesses and police said the muddy waters reached two metres in some parts of the city.
Krisna, a police official at the city's traffic information desk, said the authorities had been warned beforehand to prepare for the deluge.
"Usually local authorities have already prepared shelter, food, medical teams and clothing."
Many workers failed to reach their offices while children in parts of the city took advantage of the extreme wet weather to play and swim in the flooded streets.
Kukuh Ribudianto, of the Meteorology agency, said the downpour was affecting a large swath of West Java including Jakarta, Tangerang and the city of Bogor, home to famed botanical gardens.
Although the intensity of rain had weakened slightly overnight, it was likely to continue until the evening, said Kukuh.