Hospitals are packed with injured people in Aathbiskot municipality, Rukum West district
Security forces have been deployed to help rescue efforts in the rugged districts of Jajarkot and West Rukum, 500km (310 miles) west of Kathmandu.
Strong tremors were felt far away in the Nepalese capital and in cities in neighbouring India, including Delhi.
The army spokesman said more than 100 people had been injured. Jajarkot's hospital is packed with the wounded.
"People are scared and staying outdoors," Rabi KC, mayor of Aathbiskot municipality told BBC.
He said that they felt a very strong jolt at midnight and people rushed outdoors. "Hundreds of mud houses have been completely damaged. We are engaged in rescue and relief efforts."
Three more tremors were felt within an hour of the quake, and many people have spent the rest of the night in the open because of fear of further quakes and damage to their houses.
Video footage on local media showed crumbled facades of multi-storied brick houses. People were pictured digging through rubble in the dark to pull survivors from the remains of collapsed buildings in posts on social media.
Unicef Nepal said that they were assessing the damage and the toll of the disaster on children and families.
Nepal's Prime Minister Pushpa Kamal Dahal arrived in the affected region on Saturday, after expressing his "deep sorrow" at the loss of life and property wrought by the quake, on social media platform X. He said he had ordered security agencies to immediately launch rescue and relief operations.
But those search and rescue operations are being hampered by roads becoming blocked by landslides that were triggered by the quake.
The police chief of Jajarkot district Suresh Sunar told the Reuters news agency it was difficult to get a full picture of what had happened.
"I am out in the open myself. We are collecting details but due to cold and night it is difficult to get information from remote areas," Mr Sunar told Reuters.
"Houses have collapsed. People rushed out of their homes. I am out in the crowd of terrified residents," said another police official from the region, Santosh Rokka, who spoke to Reuters immediately after the earthquake.
The earthquake was recorded at 23:47 local time (18:02 GMT), according to Nepal's Monitoring and Research Centre.
The US Geological Survey measured the earthquake at a magnitude of 5.6, and said it was a shallow earthquake, meaning it happened closer to the earth's surface.
Nepal is situated along the Himalayas, where there is a lot of seismic activity.
Last month, a 6.3-magnitude earthquake was registered in the western district of Bajhang, resulting in injuries.
In 2015, the country suffered two devastating earthquakes in which 9,000 people were killed and 22,309 injured.
The first, on 25 April 2015, was a 7.8-magnitude quake which caused most of the damage and loss of life. A large number of aftershocks followed, including one that measured 7.3 in May of that year.
The quakes destroyed or damaged more than 800,000 houses mainly in the western and central districts, according to the International Federation of Red Cross and Red Crescent Societies (IFRC).
Government buildings, some stretches of roads and Kathmandu Valley's famous historic monuments - Unesco world heritage sites - were destroyed or damaged with many villages north of Kathmandu flattened.
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