The tremor struck at 10:37 local time (08:37 GMT) near the town of Alhendín, the IGN said. It was recorded at the depth of under 10km.
Alfonso Malpica said he felt his ground floor flat in Granada shaking in the morning.
He told Spain's El País newspaper that the quake was "stronger than the ones that happen from time to time, the ones we're used to".
"Everything came crashing down. It was terrifying," Cristina Ruiz Lopez, a lab worker who was at a supermarket in Granada, was quoted as saying by the AFP news agency.
Granada's famous Alhambra palace - a Unesco World Heritage Site of medieval Islamic architecture - "will remain closed this afternoon", the site administrators said.
It added that its team would "assess the situation" following the latest quake. The palace is visited every year by millions of tourists from around the world.
Meanwhile, Granada's metro network said it was reducing the speed of its trains to 30km/h (19mph) for "safety reasons" and warned that this may cause delays.

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