The Chief of Disaster Risk Management and National Defence at the health ministry, David Aponte, told local radio station RPP of only three minor injuries.
Following the earthquake, Arequipa was hit by four aftershocks of 4 to 4.6 magnitude, causing some landslides on local roads.
The government said on social media it was monitoring to assess the damage and "determine the actions to be taken".
The US National Tsunami Warning Center had said there was a tsunami threat from the quake, adding waves of between one and three metres above the tide level had been recorded along some parts of Peru's coast.
Prime Minister Gustavo Adrianzen, however, said the tsunami warning on the coast of Arequipa had been discarded.
Carlos Zanabria, an adviser to the regional government of Arequipa, told local radio station RPP, material damage had been reported in some districts and residents had left their homes in fear, but he had heard no reports of death or injury.
Flavio Aranguren, the mayor of Yauca district in Arequipa's Caraveli province, told RPP some walls of houses in the district had collapsed. He also said no fatalities had been reported.
Small artisanal gold mines operate in the town of Yauca and other neighbouring towns near the coast, but there was no information available so far about any impact.
Ricardo Guillen, representative of the National Emergency Operations Centre, said that there have been power and telephone line outages in areas near the epicentre of the earthquake.
Ecuador and Peru are part of the so-called Pacific Ring of Fire, an extensive area that surrounds the Pacific Ocean where clashes between the continental plates are frequent.
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