The quake struck at a depth of around 54.6 kilometres on the northwest of Timor island near the city of Kupang at around 6:30 pm local time (1030 GMT), according to the US Geological Survey.
It was strongly felt in Kupang city on Timor, an island split between Indonesian territory in the west and the sovereign state of East Timor in the east.
Residents described their houses shaking and people running outside to safety. But no damage or casualties were reported.
"The tremor was felt quite hard so I took my wife outside," said resident Elias Esi, 68.
An AFP journalist in Kupang said the quake lasted around one minute, saying "chairs were shaken and lamps inside the house were swaying".
The country's geophysics agency initially gave a higher magnitude of 6.1, before revising it down to 5.9.
Indonesia experiences frequent earthquakes due to its position on the Pacific "Ring of Fire", an arc of intense seismic activity that stretches from Japan through Southeast Asia and across the Pacific basin.
In November, a 5.6-magnitude quake hit the populous West Java province on the main island of Java, killing 602 people.
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