More than 1.2 million people likely felt strong or very strong shaking, according to the US Geological Survey (USGS).
Near the epicentre in the east of Afghanistan, around 800 people were killed and 2,500 injured in remote Kunar province alone, chief Taliban government spokesman Zabihullah Mujahid said.
Another 12 people were killed and 255 injured in neighbouring Nangarhar province, he added.
"Numerous houses were destroyed," interior ministry spokesman Abdul Mateen Qani told AFP.
The majority of Afghans live in low-rise, mud-brick homes that are vulnerable to collapse.
Some of the most severely impacted villages in remote Kunar provinces "remain inaccessible due to road blockages", the UN migration agency warned in a statement to AFP.
The Taliban authorities and the United Nations mobilised rescue efforts to hard-hit areas. The defence ministry said 40 flight sorties had so far been carried out.
A member of the agricultural department in Kunar's Nurgal district said people had rushed to clear blocked roads to isolated villages, but that badly affected areas were remote and had limited telecoms networks.
"There is a lot of fear and tension... Children and women were screaming. We had never experienced anything like this in our lives," Ijaz Ulhaq Yaad told AFP.
He said that many living in quake-hit villages were among the more than four million Afghans who have returned to the country from Iran and Pakistan in recent years.
"They wanted to build their homes here."
The quake, which struck at a relatively shallow depth of eight kilometres, was 27 kilometres from the city of Jalalabad in Nangarhar province, according to the USGS.
Nangarhar and Kunar provinces border Pakistan, with the Torkham crossing the site of many waves of Afghan returnees deported or forced to leave, often with no work and nowhere to go.
UN Secretary-General Antonio Guterres added his condolences to those shared by the Taliban government and several nations.
"I stand in full solidarity with the people of Afghanistan after the devastating earthquake that hit the country earlier today," he said.
- Frequent quakes -
After the initial quake, a series of at least five aftershocks followed throughout the night, with the strongest being one of magnitude 5.2 just after 4:00 am (2330 GMT Sunday).
Afghanistan is frequently hit by earthquakes, especially in the Hindu Kush mountain range, near the junction of the Eurasian and Indian tectonic plates.
Nangarhar province was also hit by flooding overnight Friday to Saturday, which killed five people and destroyed crops and property, provincial authorities said.
In October 2023, western Herat province was devastated by a 6.3-magnitude earthquake, which killed more than 1,500 people and damaged or destroyed more than 63,000 homes.
In June 2022, a 5.9-magnitude quake struck the impoverished eastern border province of Paktika, killing more than 1,000 people and leaving tens of thousands homeless.
Ravaged by four decades of war, Afghanistan is already contending with a series of humanitarian crises.
Since the return of the Taliban, foreign aid to Afghanistan has been slashed, undermining the already impoverished nation's ability to respond to disasters.
