The magnitude-7.1 quake hit at 4:18am (local time) on Sunday at a depth of around 10 km, the US Geological Survey (USGS) said.
Several municipalities were without electricity, and many adobe houses had collapsed, Ms Osorio said.
It said there could be waves between 0.3 to 1 metre above the tide level for Peru, and waves less than 0.3 metres above the tide level for the coasts of Chile.
A strong earthquake has struck the coast of southern Peru, causing damage to homes, collapsing roads and injuring about 20 people.
Peruvian maritime authorities said the quake did not produce a tsunami on the Peruvian coast, despite a warning initially being issued.