The earthquake, with a depth of 90 kilometers (about 56 miles), struck near the town of Kainantu on Sunday morning, the US Geological Survey reported.
The city has a population of approximately 8,500 people.
The US National Tsunami Warning Center said there was no threat of tsunami waves. Earlier in the day, it had said dangerous tsunami waves were possible 1,000 kilometers (roughly 621 miles) along the coasts of Papua New Guinea and Indonesia.
CORRECTION: An earlier version of this story quoted the Australian Red Cross as saying at least 16 people had been killed. The Red Cross has confirmed that the death toll is incorrect and is linked to a statement about an earlier earthquake in Papua New Guinea that was circulated in error.