The US Geological Survey said the magnitude-5.1 earthquake hit residential areas in Jayapura, near Papua's northern coast and was centred at a depth of 22 kilometres.
Shallow quakes often cause more damage on the Earth's surface.
"The residents were really panicked. I was in a car, and I felt like the car's wheels were lifted up," said Tri Asih, a resident of Jayapura, Papua's capital.
Officials said four people who were inside a floating restaurant died when the quake caused it to collapse into the sea on Thursday.