There were also fears of disease outbreaks in the city of at least 12 million people as drinking water pipes have been contaminated by drain water, health official Naushad Sheikh told AFP.
"According to reports we have received, at least 12 people have died in Karachi during the last 48 hours in different rain-related accidents," Sheikh said.
Three people were electrocuted by power lines that fell during the downpour and four others drowned in storm drains and floods, the private Edhi Welfare Trust said.
Karachi, Pakistan's teeming commercial hub and a major port on the Arabian Sea coast, was brought to a standstill on Monday due to flooded roads.
Pumps were installed in several area to clear the flooding but frequent power cuts caused by the rain's effect on the creaking electricity network hampered the effort.
On Tuesday most of the roads were opened for traffic, but the meteorological department has forecast another spell of widespread rain and isolated heavy showers in Sindh province during the next 24 hours.
The rain also washed away part of a railway bridge Sunday which cut the main line between Karachi and northern Pakistan. Buses were linking Karachi to Hyderabad, 160 kilometres (100 miles) to the northeast.
Torrential rain in Pakistan has killed at least 30 people in the past two weeks and caused widespread damage to crops, roads and triggered landslides.
Areas devastated by last October's South Asian earthquake are among those hit.