Most underpasses were flooded and there was nowhere to pump the flood waters out to, the chief minister for Sindh province, Murad Ali Shah said.
He said an unprecedented 126 millimeters (4.96 inches) of rain had fallen in three hours.
The streets of affluent areas such as the Defence Housing Authority complex and Clifton were flooded, with water gushing into houses.
Karachi’s main streets, which house financial institutions and bank headquarters including Pakistan’s central bank, were flooded and rescue services were using boats to reach stranded people.
The Pakistan Navy was also taking part in the relief and rescue operations.
“Deeply saddened by the tragic losses due to torrential rains in Karachi,” Prime Minister Shehbaz Sharif said on Twitter. He offered all possible support for the Karachi administration.
The highway linking Quetta city to Karachi was also closed for traffic as sections of it were swept away by flash floods.
In southwest Balochistan province, about a dozen villages in Lasbela district were submerged as the Winder River overflowed and water flooded into houses.
The Navy and local officials had rescued about 500 people and local administration from the affected villages so far, government official Farhan Suleman Ranjho said.
Last week 64 deaths occurred in different parts of Balochistan province as eight dams burst due to flood waters.
The meteorological office has forecast more rain in coming days.