The quake, at a moderate depth of 110 kilometers (68 miles) struck at 2:41 a.m., 80 kilometers (50 miles) southeast of the village of Lagunas and 158 kilometers (98 miles) east-northeast of the larger town of Yurimaguas.
There were no immediate reports of casualties, although some buildings collapsed and power cuts were reported in a number of cities. Earthquakes that are close to the surface generally cause more destruction.
In a tweet, President Martín Vizcarra called for calm and said that authorities were checking the affected areas, AP reported.
The mayor of Lagunas, Arri Pezo, told local radio station RPP that the quake was felt very strongly there, but it was not possible to move around the town because of the darkness.
In Yurimaguas, a number of old houses collapsed, and the electricity was cut, according to the National Emergency Operations Center, which gave the magnitude of the quake as 7.2.
In the capital, Lima, people ran out of their homes in fear.
Earthquakes are frequent in Peru, which lies on the Pacific's so-called Ring of Fire.