Bengkulu resident Neng Hasnah said the tremor forced her and other family members to flee her house.
Channel NewsAsia television station said it received calls from residents in Singapore, some 590 kilometers (370 miles) from Bengkulu, who also felt tremors.
No tsunami alert was issued.
There are no immediate reports of damage or tsunami warning.
Bengkulu resident Dedek Hendri said he was reading an e-book on his laptop when he felt the quake.
A strong 6.4-magnitude quake hit off the Indonesian island Sumatra on Sunday but there was no tsunami risk, seismologists said as panicked residents fled their homes.
It was felt across southern Sumatra.
National Disaster Mitigation Agency spokesman Sutopo Purwo Nugroho said the quake was felt for about 10 seconds in coastal cities and was strong enough to shake belongings from shelves and topple furniture. There are no reports of damage or casualties, however.
"As the quake got stronger, I told my wife who was cooking in the kitchen to immediately get out of the house".
He said bigger earthquakes had happened in the same epicenter in 2000 and 2007.