The driver and a pre-school teacher also died.
Local officials blamed the crash in Gansu province on the fact the bus was so overloaded, the Xinhua News Agency reported.
Gao Shaobo, head of traffic police in Zhengning county, where the nursery school is located, confirmed 20 had died and said the other 44 children were still in hospital.
Two were said to be in critical condition, while 12 had suffered serious injuries.
The impact of the crash drove the front of the orange minibus back into the seats, ripped open the top and buckled the sides of the vehicle. The lorry was only slightly damaged.
News of the crash sparked public anger across China, with hundreds of thousands of people venting on Twitter-like microblogs, highlighting an underfunded education system that especially ill serves students in remote areas.
“This accident says a lot about the problems with the government’s role of monitoring school safety,” said Liu Shanying, expert in public administration at the state-run Chinese Academy of Social Sciences. “It involves the education, traffic safety and work safety authorities.
“They should all be blamed for this. They should all be held responsible.”
“The minibus was carrying seven times as many passengers as it should have been, which meant the kindergarten should have bought seven times as many vans,” Liu added.
The bus was on its way to the Little Doctor Kindergarten on the outskirts of Qingyang city after picking up the children when the accident happened, Mr Gao said.
“The van was driving on the wrong side of the street. Both the lorry and the van were going at high speeds at the time,” he said.
The two people in the lorry were not injured though police detained the driver, Mr Gao told reporters.
Such overcrowding on school buses is common across China, and accidents happen frequently because of badly maintained vehicles and generally poor driving habits.
State television broadcast a story in September about a minivan with eight seats that was stopped while carrying 64 children.
Yesterday’s school bus accident was one of the worst in China in recent years.
In December last year, 14 children died when their school bus plunged into a river in heavy fog near the central city of Hengyang.
Crashes have become a feature of Chinese life with the rapid increase in road traffic as the economy continues to grow rapidly.
Chinese microblogs registered more than 800,000 posts within hours of the news yesterday.
“Won’t this make the government wake up?” Zhang Zhen, an editor with the popular Dahe Bao newspaper, said on the Weibo microblog.
He said the government should divert funds from public money spent on overseas travel, cars and receptions “to give middle, primary and nursery schools in poor areas more strong, decent and spacious school vehicles.”