Accompanied by torrential rain, the tornado struck the outskirts of the city of Yancheng on Thursday afternoon.
Counties on the city's outskirts saw winds of up to 125km/h (78 mph).
The search for survivors in debris has now been completed with a clean-up under way, the head of the provincial fire corps told state media.
President Xi Jinping had ordered "all-out rescue efforts" after what the Xinhua news agency said was one of the worst disasters ever to hit Jiangsu.
It was also the worst tornado to hit China in half a century, it said.
On Friday, rescuers were carrying injured villagers into ambulances and delivering food and water to others, said Xinhua.
Heavy rain and the possibility of more hailstorms and tornadoes had further complicated rescue efforts.
More than 1,300 police officers had been mobilized to help, while tent and other emergency supplies were being sent from Beijing.
'The end of the world'
Footage from the scene of the tornado showed overturned vehicles, snapped trees and street light poles, and toppled electricity pylons.
"It was like the end of the world," local resident Xie Litian told Xinhua.
"I heard the gales and ran upstairs to shut the windows. I had hardly reached the top of the stairs when I heard a boom and saw the entire wall with the windows on it torn away."
Many parts of China have been hit by torrential rains this week.
Floods in the south killed 22 people earlier this week and displaced nearly 200,000, state media said.
The southern part of China is hit every year during the monsoon season, which runs from May to July.
But this year's rainy season has been particularly wet, with water levels in some major rivers exceeding those of 1998, when disastrous floods affected 180 million people, according to state media.
Direct economic losses from the floods are estimated to be 2.7bn yuan ($410m).
Vice-Premier Wang Yang said China faced volatile weather conditions as a result of the influence of El Nino on weather patterns. (BBC)