The powerful quake triggered a tsunami warning but the alert was lifted an hour later.
A mother and her child were killed when their house collapsed in Serui district on Yapen island, said Andreas Suleyman, a local policeman.
The quake also sparked fires in six houses and damaged a church and a school, he said.
'Some residents have fled to the mountains because they are afraid there will be a tsunami,' he said.
The quake occurred at 12:16 p.m. (0316 GMT), with an epicentre about 123 km south-east of Biak at a depth of 10 km, the Meteorology and Geophysics Agency said.
It was preceded by a magnitude-6.2 quake around the same area and followed by another measuring 6.6 on the Richter scale, sparking panic in Biak and Manokwari districts.
'We felt the ground and the building shaking strongly,' said Ibnu Sulistyono, an official at the Meteorology and Geophysics Agency in Biak.
'People ran out of their homes but I haven't seen any damage around here,' he added.
A Biak resident named Yuliana told Metro TV by telephone that coastal residents were ready to flee to higher ground.
'When the second quake hit, people suddenly stopped working and panicked,' she said.
A magnitude-9.2 quake struck in December 2004 off Sumatra and caused a tsunami that spread death and destruction across the Indian Ocean. More than 170,000 people perished in Aceh province alone.
Indonesia sits on the so-called Pacific Ring of Fire, one of the most active areas for earthquakes and volcanic activity in the world.