The quake hit at a depth of 31 kilometres (19 miles) off Sumba island, some 150 kilometres west southwest of the city of Waingapu, according to the United States Geological Survey.
It was followed by a weaker quake in the same area with an initial reading of 5.2 magnitude, according to Indonesia's disaster agency.
There were no immediate reports of damage or casualties.
Indonesia is still reeling from a deadly tsunami at the end of December triggered by an erupting volcano in the middle of the Sunda Strait between Java and Sumatra islands that killed more than 400 people.
The vast Southeast Asian archipelago is one of the most disaster-hit nations on Earth due to its position straddling the so-called Pacific Ring of Fire, where tectonic plates collide.
The tsunami was Indonesia's third major natural disaster in six months, following a series of powerful earthquakes on the island of Lombok in July and August and a quake-tsunami in September that killed around 2,200 people in Palu on Sulawesi island, with thousands more missing and presumed dead.