The undersea earthquake occurred at 03:21 am (2021 GMT Monday) with the epicentre 19 kilometers (12 miles) south of the town of Lumajang in East Java province, said Subagyo of the National Meteorology and Geophysics Agency.
Residents in Lumajang contacted by AFP said they were not aware of the quake.
Indonesia, a sprawling archipelago of thousands of islands, lies at the junction of three major tectonic plates that cause frequent earthquakes and trigger regular volcanic eruptions.
A 9.0-strong earthquake off Indonesia's Sumatra island on December 26 produced tsunamis that left about 280,000 people missing or dead around the Indian Ocean.
On January 24 a 6.2-strong earthquake jolted the town of Palu on Sulawesi island, damaging dozens of homes and prompting thousands to flee to higher ground fearing a tsunami.