Pictures show landslides and ruined mud-built homes in eastern Paktika province, where rescuers are scrambling to treat the injured.
In remote areas, helicopters have been ferrying victims to hospitals.
Taliban leader Hibatullah Akhundzada said hundreds of houses were destroyed and the death toll was likely to rise.
"Unfortunately 300 civilians have been martyred and more than 500 injured," he added.
Another Taliban official - deputy minister of disaster management - told a news conference that the death toll was as high as 920.
The quake struck about 44km (27 miles) from the south-eastern city of Khost shortly after 01:30 local time (21:00 Tuesday GMT), when many people were at home, asleep in their beds.
Earthquakes tend to cause significant damage in Afghanistan, where there are many rural areas where dwellings are unstable or poorly built.
Taliban officials called for aid agencies to rush to the affected areas in the nation's east.
Decades of conflict have made it difficult for the impoverished country to improve its protections against earthquakes and other natural disasters - despite efforts by aid agencies to reinforce some buildings over the years.
Even before the Taliban takeover, Afghanistan's emergency services were stretched to deal with natural disasters - with few aircraft and helicopters available to rescuers.
Most of the casualties so far were in the Gayan and Barmal districts in Paktika, a local doctor told the BBC. Local media site Etilaat-e Roz reported a whole village in Gayan had been destroyed.
Tremors were felt across more than 500km of Afghanistan, Pakistan and India. Witnesses reported feeling the quake in Afghanistan's capital, Kabul, as well as Pakistan's capital, Islamabad.
However, there have been no immediate reports of casualties, and the earthquake caused little damage in Pakistan, according to BBC Urdu.
Afghanistan is prone to quakes, as it's located in a tectonically active region, over a number of fault lines including the Chaman fault, the Hari Rud fault, the Central Badakhshan fault and the Darvaz fault.
The earthquake was magnitude 6.1 at a depth of some 51km, according to seismologists.
In the past 10 years, more than 7,000 people have been killed in earthquakes in the country, the UN's Office for the Coordination of Humanitarian Affairs reports. There are an average of 560 deaths a year from earthquakes.
