The earthquake hit the island at 06:35 GMT. According to the EMSC, the epicentre was located at a depth of 30 kilometres (18.6 miles), 35 kilometres south-east of the city of Mamuju.
Though no official information on damage or injuries has been reported so far, some Twitter users post videos of destroyed structures.
Just two days ago, Indonesia's Irian Jaya was hit by another 5.7-magnitude earthquake.
The country is situated in the so-called Ring of Fire, a region around much of the rim of the Pacific Ocean with high volcanic activity, and is frequently hit by earthquakes.