The international charity says nine out of 10 schools have been destroyed in the worst-affected districts.
Almost 24,000 classrooms were damaged or destroyed in the disaster that hit the country 12 days ago, it adds.
Unicef is attempting to set up temporary learning spaces for children.
Currently, all schools are closed in Nepal, although many of those still standing are being used as emergency shelters.
They are due to reopen on Friday, 15 May.
As the humanitarian and clear-up efforts continue, the charity says there is a desperate need to set up alternative learning spaces for children, not just for education but for their safety as well.
Unicef spokesman in Kathmandu Kent Page told the BBC: "We know that children need to go to school not only to learn, but schools are places of protection for children who have been through the trauma of an earthquake.
"It protects them from exploitation and abuse because everybody knows what they are doing and where they are.
"Unicef has already set up 30 child-friendly spaces in temporary camps and settlements in Kathmandu.
"These are places where in children can play and learn and sing and dance in a protected environment."
Mr Kent said he had visited children in the settlements in the past few days, and all those he had asked whether they wanted to return to school had said they did.
"They want to be in school, they want to be learning, they want to get back to normal as much as their parents do," he said.
Unicef's representative in Nepal, Tomoo Hozumi, said temporary learning places needed to be provided as soon as possible to avoid a massive school drop-out.
He said: "Almost one million children who were enrolled in school before the earthquake could now find they have no school building to return to.
"There is a desperate need to set up alternative learning spaces, assess and repair buildings, and mount a public awareness campaign encouraging families to send their children back to school and pre-school.
"Prolonged interruption to education can be devastating for children's development and future prospects," he added.
In Nepal, children aged between five and nine are given free education between 09:30 and 15:00 daily.
There has been a large increase in the number of children enrolled in school in Nepal in the past three decades.
In 1990, 64% of children attended school. This had risen to 95% of children by this year, Unicef said.
Nearly a million children in Nepal will not be able to return to school in the wake of last month's earthquake unless urgent action is taken, says Unicef.