"There are two fatalities in the region of Arequipa and so far 65 injured have been reported", General Jorge Chavez, head of the National Civil Defense Institute, said.
The governor of Peru's Arequipa said that there was minor material damage after the quake, non-serious damage to some roads.
INDECI also said that 65 had been injured in the quake.
The quake struck 42 kilometers (26 miles) south-southwest of Acari at 0918 GMT on Sunday, USGS reported.
An informal mine east of the coastal city of Chala collapsed following the quake, after which 17 people were missing, Peru's health minister said.
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Several municipalities were without electricity, and many adobe houses - houses built with earth - had collapsed, she said. Many residents of Lomas, a coastal town, were evacuated after feeling an aftershock. There have been no immediate reports of casualties or damage.
The threat of a tsunami was ruled out by the Peruvian navy and the Pacific Tsunami Warning Center in Hawaii.
In 1970 Peru faced the worst natural disaster in its history - the Ancash quake, more commonly known as the Great Peruvian quake.
Peruvian maritime authorities said the quake did not produce a tsunami on the coast.