The Tanimbar islands are a group of about 30 islands in eastern Indonesia's Maluku province.
At least four aftershocks were reported after the powerful quake that was also felt in some parts of northern Australia, Reuters reported.
Indonesia disaster agency officials said that at least 15 homes and two school buildings were damaged, with one person injured, after the tremor was felt strongly for 3-5 seconds.
The quake, locally measured as magnitude 7.5, struck at a depth of 130 km (80.78 miles) at 2:47 a.m. local time, the country's geophysics agency BMKG said. The tsunami warning was lifted at 5:43 a.m.
"Based on our observation of four tide gauges around the earthquake's epicentre ... there was no anomaly detected or no significant changes of sea level," BMKG head Dwikorita Karnawati told a news conference, advising people who lived near the coast to continue with their activities.
RHM/PR