The first, 6.2-magnitude, quake struck about 1:10 pm (local time) on the small island of Biak, followed quickly by three more in the same area, the largest being at magnitude 7.1.
Indonesia's meteorological agency said the quakes occurred at a depth of 10 kilometres.
“We have been informed that there are two dead victims but not yet identified,” said a local police officer in Serui of Yapen in Papua.
On Biak, fear of a tsunami drove hundreds of people from their homes for higher ground, away from the coastline.
Earlier, one victim was reported killed by another earthquake in West Sulawesi, as tens of homes were destroyed in Lambara Village of Baras Sub District in North Mamuju.
“The victim was killed as his body was covered by huge sand deposit while a moderate quake jolted this early morning,” said Saidiman Marto, a spokesman for North Mamuju district.
Earlier in the week, a far greater quake of 7.5 Richter hit the westernmost province of Aceh, but it did not claim any lives or cause any major damage.
The Indonesian Archipelago is located along the so-called Pacific ‘Ring of Fire’, which is seismically very active.
In 2004, Aceh was hit by 9.3-magnitude quake and a powerful tsunami that claimed 250,000 lives in 13 Asian nations, including Indonesia, Sri Lanka, India and Thailand.