Most of the deaths were reported in Karachi, the country's largest city and its commercial hub. The port city on the Arabian Sea had at least 600 fatalities.
Temperatures reaching 458 Celsius (1138 Fahrenheit) first struck over the weekend in Karachi, with mercury rising in the rest of Sindh province. Hours-long power outages, typical in Pakistan, left fans and air conditioners inoperable.
The heat wave compounded the struggles of ordinary Pakistanis as it struck amid the holy, fasting month of Ramadan when observant Muslims abstain from food or water during daylight hours.
"We have confirmed data that 622 people died of the heat wave across the whole of province," said Saeed Mangnejo, the top administrative health official in Sindh.
"But the worst hit is Karachi, where over 600 people died of heat stroke; 19 died in other parts of the province," he said, adding that he expected the number of fatalities to climb even further.
"Many people have been taken to private hospitals where they have died ... we are collecting that data," Mangnejo said.
Most of the dead are the elderly, said Seemi Jamali, a spokeswoman for Karachi's Jinnah Hospital. Thousands more are being treated for heat-related ailments, including fever and dehydration and stomach-related illnesses, she said. Mortuaries were running out of space, with local television stations showing bodies stacked inside of cold-storage rooms of morgues.