It was followed by another big quake and a string of aftershocks.
Witnesses said the tremors triggered mass panic in Manokwari, where several buildings were flattened.
A tsunami alert was issued by Indonesian authorities following the earthquakes, but withdrawn within an hour.
Assessment teams and medical supplies are expected to arrive in the remote region, some 2,955km (1,830 miles) east of Indonesia's capital Jakarta, within the next 24 hours.
The first quake struck on land about 95 miles (150km) north of Manokwari at a depth of 22 miles (35km), the US Geological Agency said. It was followed by another tremor and aftershocks.
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The BBC's Lucy Williamson said eyewitnesses described crowds of people running terrified through the streets of the region's main city amid fears of a tsunami.
Among the four victims of the quakes was a 10-year-old girl who was crushed by a falling wall, officials said.
At least 37 people were injured and were being treated in hospitals.
An official with the World Vision aid organisation said 10 buildings had been totally destroyed, including several hotels and the house of a government official.
Officials said three people, who had been staying at the Mutiara hotel in Manokwari, were pulled alive from the rubble and taken to hospital.
Electricity was also cut off in the city with a population of some 160,000 people.
Japan's Meteorological Agency told Reuters news agency the earthquakes also triggered a small tsunami which hit the Japanese coast, but did not cause any damage.
A huge quake off western Indonesia on 26 December 2004 caused a massive tsunami that killed around 230,000 people around the region.