But officials confirmed no casualties or serious damage, notably to the southern city's Alhambra palace, a UNESCO-listed jewel of medieval Islamic architecture and the seat of Spain's last Muslim kingdom.
The tremor took place shortly after 1:00 am (2300 GMT Friday) with its epicentre in the town of Alhendin, 10 kilometres (six miles) south of Granada, according to the National Geographical Institute.
"Cracks have appeared, elements such as ledges, rubble and walls have fallen and damage has been reported in some buildings," Andalusian emergency services said in a statement.
The fire service received 300 calls and performed 85 interventions, especially in southern Granada and the city's metropolitan area, said Antonio Sanz, the Andalusia region's top emergencies official.
"There is no serious structural damage, no serious material damage and there are no casualties," said Sanz, who specified that "the Alhambra had not been affected in any way".
But "we must stay on our guard" as buildings were being inspected and aftershocks were possible, Sanz added, noting that the last earthquake of this magnitude in Andalusia hit in 1955.
An AFP journalist in Granada saw a pile of broken tiles that had fallen from a church's roof, with tourists stopping to take photos of the cordoned-off site.
Images shared by Spanish media showed rubble strewn on the streets and cars with their windows smashed.
"We really felt the shaking, it was so strong that it woke us up," Marta Mayorga Fernandez told public broadcaster RTVE from the town of Huetor Vega, just outside Granada.
"We were here at home panicking a little, in our bodies, my arms were still shaking," she said.
Sanz said a telephone line had been set up to "allow us to immediately deal with these anxiety crises, this nervousness among the public".
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