About 60,000 people have already shifted to higher ground, including many residents of two offshore islands, according to Hamal Kalmati, a government minister in Baluchistan province.
Kalmati said many mud houses in Gawadar and Pasni districts had already collapsed, and another provincial official said 18 people have been injured so far.
Tropical Storm Phet was originally of cyclone strength; it hit Oman first and killed at least 16 people. Omani authorities have yet to announce the total cost of damages caused by the storm.
In Karachi, hours of rain on Sunday left roads under more than 30cm of water. Electricity was cut in many districts in the mostly low-lying city of 18 million people.
Many parts of Karachi and other towns along Pakistan's coast are desperately poor. Roads, bridges, houses and drainage systems are already in bad condition, making them vulnerable to high winds, heavy rain and rough seas.
Sualeh Farooqi, the head of Sindh province's disaster management authority, said Karachi's poor infrastructure would be heavily impacted by the storm.
Hundreds of relief camps have been set up throughout the province, but some local residents have complained about a lack of facilities at those camps.
"My family had gone to a relief camp a couple of days ago, but there was not enough food and medical facilities, which forced us to come home," Mohammad Hashim, a resident of Karachi's Rerhi Goth neighbourhood, told the AFP news agency.