There were no immediate reports of injuries following the quake which the US Geological Survey said struck at a depth of 110 kilometers (68 miles).
"Some casualties and damage are possible and the impact should be relatively localized," USGS said in a preliminary assessment.
Quakes of similar depth "typically cause less damage on the ground surface (but)... may be felt at great distance from their epicenters," it later added.
The tremors were felt in northern and central Peru, including the capital Lima, where terrified residents ran out of their homes.
The mayor of Lagunas, Arri Pezo, said many residents were too scared to venture back indoors for fear of aftershocks.
"You could not walk at the time of the earthquake, things were falling," Pezo told the RPP radio network, adding that it was difficult to determine any damage because the electricity supply had been knocked out.
Peruvian President Martin Vizcarra urged citizens "to remain calm" in a message on his official Twitter account.
"We're evaluating the affected areas," he said.
The Ministry of the Interior said on its official Twitter page that no injuries or deaths had been reported, but some houses had collapsed.
Hugo Araujo, the mayor of the city of Yurimaguas near the epicenter, said, "there are many old houses that have collapsed after this strong earthquake."
Seismologists at the Geophysics Institute of Peru said the quake, which lasted just over two minutes, measured 7.5 magnitude, revising their earlier assessment of 7.2 magnitude.
Experts at the US-based Pacific Tsunami Warning Center said there was "no tsunami threat because the earthquake is located too deep inside the earth."
Power cuts in Ecuador
The shockwave of Sunday's tremor also extended to neighboring Ecuador, where power cuts were reported in parts of the Amazon region.
"We have carried out the respective monitoring in each city to collect information and report damage after the earthquake, so far we have no news," wrote Ecuadorian Vice President Otto Sonnenholzner on his Twitter account.
The president of Ecuador, Lenin Moreno, who is in Lima to attend a regional summit later on Sunday, tweeted that the town of Yantzaza had experienced power cuts, adding that officials would provide more information about the quake's impact as it became available.
Peruvian media said the tremor was also felt in parts of Colombia and Venezuela.
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.
The South American country records about 200 earthquakes a year, most of them going unnoticed by the public.
In February a quake measuring 7.5 with its epicenter in Ecuador rattled the coast and Amazon region of northern Peru.
It left nine people injured and caused damage in Ecuador, but Peru was unscathed. (AFP)