People make their way through a flooded road from heavy monsoon rains in Karachi [Rehan Khan/EPA]
Rescue official Anwar Kazmi said seven people died from electrocution and three people died after a roof collapsed in Karachi city of 20 million people.
The death toll was expected to rise as roads and streets were still flooded in some parts of the city, making it impossible for rescuers to reach the victims, Kazmi added.
The military was assisting the civil administration in pumping the water out of the inundated streets, an army spokesperson said.
According to the Met Office, Karachi is expected to receive intermittent rain during the next 24 hours.
Police officer Idrees Khosa said five people died in a flash flood and another two were electrocuted in Punjab province, which also saw heavy rains.
Pakistan often struggles to cope with the annual monsoon, which runs from July to September and causes flooding across South Asia.