The shallow quake struck about 165 kilometres (100 miles) south-southwest of the town of Ternate in North Maluku province at 6.28pm (0928 GMT/5.28pm Malaysian time), according to the US Geological Survey.
The quake occurred at a depth of 10km in an area 168km south-southeast of the city of Ternate, the US Geological Survey said.
There were no immediate reports of casualties from the quake.
Some people sent the night outdoors as numerous aftershocks rocked the Maluku island chain where the quake was most strongly felt.
The shallow quake struck at a depth of 10 kilometers (6 miles), according to USGS.
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With a population of around 1 million, North Maluku is one of Indonesia's least populous provinces.
Hundreds of people are still sheltering in several schools, government buildings and higher grounds. "Some people who live near the ocean are starting to move to higher ground", he told Reuters by phone.
Earlier Sunday, an natural disaster of magnitude 6.6 struck west of Australia's beach resort of Broome, the United States Geological Survey said, with residents saying the impact shook some buildings and pushed groceries off shelves. Last year, more than 2,200 were killed in a 7.5-magnitude quake and a subsequent tsunami in Palu on Sulawesi island.
Eastern Indonesia has been hit by a magnitude 7.3 natural disaster.
A strong, shallow quake struck eastern Indonesia's North Maluku province on Sunday, causing panic in several cities and villages.
The province was also hit by a 6.9-magnitude tremor last week but no extensive damage was reported.