The quake on Sunday initially sparked a tsunami warning for some coasts in Peru and neighbouring Chile, but this was quickly called off.
Its epicentre was in the Lomas district, in the southern region of Arequipa.
Arequipa governor Yamila Osorio said on Twitter that a 55-year-old man had been killed after being struck by a falling rock, while 20 others suffered "light injuries" in the town of Cacha.
Jorge Chavez, chief of Peru's Civil Defense Institute, told local radio station RPP that a second death was reported in the town of Bella Union; however, this statement was later reversed, according to reports.
Several municipalities have been left without electricity, while many roads and houses have collapsed, Ms Osorio said.
Residents of Lomas were evacuated after feeling an aftershock, she said.
The earthquake destroyed 63 homes and displaced about 130 people, injuring 65.
"Everything that is needed is going to be sent," Peru's President Pedro Pablo Kuczynski said.
"We are already responding at full speed."
Emergency crews have responded by getting tents and mattresses to displaced people.