The school bus was carrying children as young as five or six on their way to Ramallah, just north of Jerusalem.
The vehicle overturned on impact and burst into flames. More than 30 children were injured, and there are fears the death toll may rise.
Israeli Prime Minister Benjamin Netanyahu has expressed his sorrow and offered assistance.
The bus is believed to have been carrying up to 50 children at the time of the crash, which happened on a busy road junction.
At least one report said a teacher had also been killed.
“The toll so far shows that more than 10 children have died and scores of injured are receiving treatment in various medical centres in the West Bank,” he said.
The higher figure of the number of dead has not been confirmed.
The children were apparently travelling from their school in the West Bank village of Anata when the two vehicles collided, head-on, according to reports.
The lorry driver, an Israeli-Arab, was injured.
Dr. Ahmad Bitawi, director of Ramallah Hospital, said five children and a teacher had been pronounced dead at the hospital, while a further 54 people injured in the crash were treated there, Reuters news agency reported.
Some of the survivors were also taken to Jerusalem’s Hadassah University Hospital.
“It is an ugly, unbelievable, terrible accident; it shakes the feelings of the whole world because it includes babies,” Adham Al-Hindin, uncle of two injured children, told Reuters.
Shalom Galil – an Israeli paramedic at the scene – also said the adverse weather conditions appeared to have been a factor.
He said the steep road where the crash happened had been affected by oil. “We assume that either the bus or the truck slipped and crashed into each other.”
Shalom Galil said Israeli and Palestinian emergency services had worked closely together at the scene.
“Palestinian firefighters were involved. As far as I could see, there was full co-operation between the firefighters of Judea and Samaria [West Bank] and the Palestinian firefighters.”
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