The US Geological Survey said the epicentre of the 7.5-magnitude earthquake was in the Hindu Kush mountains, in the sparsely populated province of Badakhshan, which borders Pakistan, Tajikistan and China.
It said the epicentre was 130 miles deep and 45 miles south of the provincial capital, Fayzabad.
At least 12 students at a girls' school inTakhar province, west of Badakhshan, were killed in a stampede as they fled shaking buildings, said Sonatullah Taimor, the spokesman for the provincial governor.
Another 42 girls were taken to the hospital in the provincial capital of Taluqan.
In eastern Nangarhar province, eight people died and 78 were wounded. Hazrat Hussain Mashreqiwal, spokesman for the provincial police chief, said several houses were destroyed in Jalalabad city, with destruction also reported in some rural districts.
In Pakistan, Abdul Latif Khan, an official at the Provincial Disaster Management Authority, said the quake killed 48 in the north-western Khyber Pakhtunkhwa province alone. Another official, Mussarrat Khan, said 16 people were killed in the country's tribal regions bordering Afghanistan.
The toll from the sparsely populated Badakhshan province was likely to rise as reports came in from remote areas. The province is often struck by earthquakes, but casualty figures are usually low.
The Pakistani Prime Minister Nawaz Sharif is cutting his visit to London short and returning home according to local news.
Meanwhile Google has launched a person finder to help track missing persons in the earthquake.
Police said dozens of houses had been destroyed in two remote and sparsely populated rural districts in Badakhshan, with some damage reported in Fayzabad.
Afghanistan's Chief Executive Abdullah Abdullah called an emergency meeting of the disaster management authority to assess the damage, his senior adviser Omar Samad tweeted.
Mr Abdullah later tweeted that the meeting would assess damage in one of Afghanistan's most vulnerable regions.
Power was cut across much of the Afghan capital, where tremors were felt for around 45 seconds. Houses shook, walls cracked and cars rolled in the street. Officials in the capital could not be immediately reached as telephones appeared to be cut across the country.
Footage shows the Afghan TV station Afghan Ariana being knocked off air by the quake. The presenter can barely keep his balance as the tremors take hold.
لحظه #زلزله در پخش زنده تلویزیون آریانای #افغانستانAfghanistan #earthqake live on TV
Pakistan's army chief, Gen Raheel Sharif, ordered troops to the quake-affected areas, the military said.
The quake was also felt in the Indian capital New Delhi, though no damage was immediately reported. Office buildings swayed and workers who had just returned from lunch ran out of buildings and gathered in the street or car parks.
In Srinagar, the main city in the India-controlled portion of disputed Kashmir, the tremors lasted at least 40 seconds, with buildings swaying and electrical wires swinging wildly, residents said.
"First I thought somebody had banged the door. But within seconds, the earth began shaking below my feet, and that's when I ran out of the building," said government official Naseer Ahmed.
People ran outside, shouting, crying and chanting religious hymns in an effort to keep calm. "I thought it was the end of the world," shopkeeper Iqbal Bhat said.
Srinigar police Inspector General Syed Javaid Mujtaba Gilani said there were no immediate reports of casualties, but that "some bridges and buildings have been damaged," including a cracked highway overpass.
Two elderly women died from heart attacks suffered during the earthquake, including a 65-year-old woman in the northern Kashmiri town of Baramulla and an 80-year-old in the southern town of Bijbehara, officials said.