Reportedly, a tsunami warning has also been issued.S
The quake hit 75 kilometres (47 miles) south-west of the town of Panguna on Bougainville island, USGS said.
A tsunami warning was issued for Papua New Guinea and Solomon Islands, the Hawaii-based Pacific Tsunami Warning Center said.
The quake struck at a depth of 30 kilometres just before 11:30 pm (1330 GMT), USGS said. Another 5.6-magnitude quake had happened around 20 minutes later in the same area at a depth of 69 kilometres.
A 6.6-magnitude quake occurred in the same area on Saturday morning, USGS reported earlier.
Papua New Guinea is located on the region known as Pacific Ring of Fire, which is a hotspot for seismic activity due to friction between tectonic plates.