At least 51 people are said to have been killed in Pakistan, with 19 deaths reported in Afghanistan.
According to the US Geological Survey, the tremor was centered in the mountainous Hindu Kush region, 46 miles south of Faizabad.
Buildings were evacuated in the capitals of all three countries and communications disrupted in many areas.
In the Afghan province of Takhar, a stampede at a girls’ school triggered by the quake left 12 students dead and another 25 were injured, local reports said.
Seven people have been reported killed and 71 injured in the eastern Afghan province of Nangarhar.
In Pakistan, 28 people have been killed in the northern tribal areas, another 20 in the north-west and three more in the Gilgit-Baltistan region, officials told AFP news agency.
Officials said the quake happened at a depth of 212km. The magnitude was initially put at 7.7 but later downgraded.
An aftershock measured at 4.8-magnitude struck shortly afterwards.
People in the Indian capital Delhi ran into the streets after the tremor struck, and schools and offices were evacuated. The Delhi metro was also briefly halted.
Indian PM Narendra Modi tweeted that he had ordered an urgent assessment of any damage.
“We stand ready for assistance where required, including Afghanistan and Pakistan,” he said.
The region has a history of powerful earthquakes caused by the northward collision of India with central Asia.
In 2005, a magnitude 7.6-magnitude earthquake in Pakistan-administered Kashmir left more than 75,000 people dead.
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