The quake was about 158 kilometres (98 miles) south-southwest of the province's capital Jayapura at 6:42 pm (0942 GMT), at a depth of 61 kilometres, according to the US Geological Survey.
The quake was felt in Jayapura, but residents didn't panic, a military spokesman said.
"I felt it at home," Papua's military spokesman in Jayapura Dax Sianturi said.
Officials are still assessing the impact of the quake, but there were no immediate reports of casualties.
Indonesia experiences frequent seismic and volcanic activity due to its position on the Pacific "Ring of Fire", where tectonic plates collide.
Last September, a 7.5-magnitude quake and a subsequent tsunami in Palu on Sulawesi island killed more than 2,200 with a thousand more declared missing.
On boxing day December 26, 2004, a 9.1-magnitude earthquake struck Aceh province, causing a tsunami and killing more than 170,000 in Indonesia.