The 7.5-magnitude tremor struck 90 kilometres south of Porgera in the Pacific nation's Enga province early Monday, with two strong aftershocks rattling the rugged region.
Phone lines were largely cut, but the PNG Post Courier newspaper cited Hela provincial administrator William Bando as saying there were casualties.
It reported that at least 13 died in the Southern Highlands capital Mendi while 18 others were believed to have been killed in nearby Kutubu and Bosave.
Some 300 people were injured, it added, and properties damaged, with reports of landslides and sinkholes.
The Papua New Guinea Today website, quoting Catholic priest Pius Hal, said at least 10 died, including four children, in quake-triggered landslides.
A government assessment team was due to fly into the area today to get a better idea of the impact, with the military mobilised to help restore services and infrastructure, the government's Chief Secretary Isaac Lupari said in a statement.