The tremor comes after a 7.5-magnitude and subsequent tsunami struck off the Indonesian island of Sulawesi - around 1000km northeast of Situbondo - last month, killing more than 2000 people.
It was followed by a second magnitude 7.0 quake near Papua New Guinea, prompting the Australian Bureau of Meteorology to issue a message there was no tsunami threat to Australia.
Disaster agency spokesman Sutopo Purwo Nugroho said that victims were crushed by collapsed buildings while they were asleep.
No tsunami warning was issued for the natural disaster.
According ot the US Geological Survey, the magnitude 6.0 quake's epicentre was about 40 km north-east of Sumberanyar on nearby Java island.
Aside from the Asean event, Bali is also due to host the International Monetary Fund and World Bank's respective annual meetings this week. He added that the damage from the quake was minor.
Bali is now hosting the 2018 Annual Meetings of the International Monetary Fund (IMF) and the World Bank Group.
Finance Minister Asad Umar later had a meeting with World Bank President Dr Jim Yong Kim.
People in the eastern part of Java, Madura and Bali islands also reported they felt the natural disaster. People on the island were reported to have briefly panicked and fled their homes.
Indonesia's disaster agency says it only needs tents, water treatment units, generators and transport from other countries as it responds to the Sulawesi quake and tsunami that killed more than 2,000 people. Around 5,000 people were thought to still be missing. "Here in Bali, the quake has not caused significant damage nor any disruption to the meetings", an International Monetary Fund spokesman said.
The country was still reeling from an natural disaster and tsunami last month that killed more than 2000 people.
Indonesia, one of the most disaster-prone nations on earth, straddles the so-called Pacific "Ring of Fire", where tectonic plates collide and numerous world's volcanic eruptions and earthquakes occur.
Site highlights each day to your inbox.