There were no immediate reports of injuries or damage.
The Volcanic Ash Advisory Centre in Darwin said the ash cloud was drifting southeast and had the potential to disrupt air travel.
"The eruption was to 60,000 feet [18,288m], which is flight level. There was two hours of high-level eruption," an official from the centre, Cyndee Feals, told AFP.
"The ash was initially blowing to the southwest but has now turned to the southeast and we expect it to clip the edge of Australian airspace later today, but we don't expect ash over Australia."
She said planes may be forced to take alternative routes with the ash forecast to move towards the Solomon Islands and then Vanuatu in the Pacific.
In Rabaul, the ground was covered in a layer of ash, local reports said.
"Police have cautioned people not to panic but remain indoors and listen to local Radio East New Britain for updates," the PNGloop website said.
"The situation has eased except for the rumbling and roaring as rocks are shot into the air."
The 688m volcano has erupted several times before. In 1994, major eruptions at both Tavurvu and nearby Mount Vulcan destroyed much of Rabaul, and while loss of life was minimal due to a quick evacuation, looters ransacked the town.
AFP