The quake struck at a depth of 10 km (6.21 miles).
"Please move away from beach and move to higher ground," BMKG said in a text message, noting that the warning applied especially to Seram Island.
A tsunami wave could potentially be triggered by underwater landslides, it added. It earlier said there was no tsunami potential.
A local disaster mitigation agency official said there were no report of injured people or casualties so far, but some buildings and public facilities sustained damage.
Unverified videos that circulated online showed some local residents moving to higher ground after the quake.