The 7.8 magnitude quake struck an area of central Nepal between the capital, Kathmandu, and the city of Pokhara.
There were also victims in India, Bangladesh, Tibet and on Mount Everest, where avalanches were triggered.
The government has declared a state of emergency in the affected areas, and help has been offered by countries around the world.
Little information has emerged from the epicentre, where extensive damage has been reported, and there are fears the death toll could rise yet further.
The Nepalese information minister has told the BBC that 1,500 people had been killed in the disaster, but that the true casualty figure would probably be much higher.
Thousands of people are spending the night outside their houses, following a series of aftershocks.
Many more people are trapped under rubble. Local television pictures showed rescuers in Kathmandu desperately digging through the rubble with their bare hands in search of survivors. Many historic buildings in the capital were also destroyed.
Eyewitness: Sandesh Kaji Shrestha, Kathmandu
Kathmandu has been very badly affected by the earthquake. Some areas are completely destroyed.
I am in the Thamel area and the Hotel Budget has been completely demolished with more than 50 guests inside.
I have been helping to pull people and bodies out of the rubble, along with my friend. We pulled a child out with its grandmother earlier. They did not survive.
I am most sad. It has been a very bad experience and a terrible and very difficult day.
There are not enough rescue teams here. The hospitals are out of control. We need help.
The quake triggered an avalanche on Mount Everest, killing at least 10 people, and another five in Tibet, officials and reports say.
At least 40 people have been killed in India, Indian officials say, with one death also reported in Bangladesh.
It is the worst earthquake to strike Nepal since one in 1934 which killed some 8,500 people.