Ms Osorio said on Twitter the quake caused minor material damage, including some collapsed roads.
A 7.1-magnitude quake shook the coast of Peru on Sunday at 4:18 a.m. local time.
Peruvian President Pedro Pablo Kuczynski headed to Arequipa region to inspect the damages caused by a 6.8-magnitude natural disaster in the area.
"There are two fatalities in the region of Arequipa and so far 65 injured have been reported", INDECI chief Jorge Chavez said, adding that the toll was likely to rise.
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Earlier, the Pacific Tsunami Warning Center warned of "hazardous tsunami waves" for some coasts, saying there was a threat to some coasts of Peru and neighboring Chile. However, all warnings were canceled an hour after the quake because tsunami waves were not observed.
Peru is located in the Ring of Fire, which is an area in the Pacific Ocean vulnerable to earthquakes and volcanic eruptions. A 2007 quake in the country's southern Ica district killed 595 people.
The area between the South America and Nazca plates, where the tremor occurred, is prone to earthquakes, with 13 above magnitude 6.5 occurring over the past century, the US Geological Survey says.