Officials say a man has died and 20 other people are injured, with damage to roads and houses and some areas left without power.
Homes made of adobe collapsed in coastal areas most directly affected by the quake, local authorities said.
According to the US Geological Survey, the quake struck at a depth of 36.3 km and no tsunami alert has been activated so far.
Several municipalities lost electricity, and many roads and adobe houses collapsed, Osorio said.
Chile's National Emergency offices said there were no reports of injuries, damage to infrastructure, or interruption of basic services.
Earthquakes are common in Peru, but many homes are built with precarious materials that can not withstand the tremors.
The U.S. Pacific Tsunami Warning Center initially warned of that hazardous waves could hit Peru and Chile, but later stated there was no longer any tsunami threat from the quake.
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In the city of Arequipa, residents ran into the streets after the quake struck at 4:18 am (0918 GMT).
Peru lies on the so-called "Ring of Fire" - an arc of fault lines that circles the Pacific Basin and is prone to frequent earthquakes and volcanic eruptions.
However, Interior Minister Vicente Romero said the disaster would not affect Pope Francis' scheduled visit for this coming Thursday through next Sunday.
The South American country records about 200 earthquakes a year, majority going unnoticed by the public.
The regions of Arequipa, Ica and Ayacucho have been affected.
An natural disaster with a preliminary magnitude of 7.3 struck off Peru's coast at 0918 GMT (4:18 a.m. EST).