Hundreds of buildings were damaged when the 6.5-magnitude earthquake struck on Friday evening.
A 62-year-old man and an 80-year-old woman lost their lives when the buildings they were in collapsed, and a 34-year-old woman died when she fell while running out of her house.
Indonesia's national disaster management agency says seven others were injured.
Dozens were evacuated after a hospital suffered damaged ceilings, cracked walls and leaks to oxygen pipelines - with about 70 patients given shelter in tents.
The densely populated island of Java is home to more than half of Indonesia's 250 million people - and photographs posted on Twitter show people scouring through collapsed buildings.
Tremors from the earthquake lasted for up to 30 seconds and were felt 125 miles away in the capital, Jakarta, where high-rise buildings swayed for several seconds, prompting those inside to leave their homes.
People fled coastal areas in fears of a tsunami, clogging local roads. But no big waves were reported and a tsunami warning was lifted two hours later.
A food vendor in the Sukabumi region, Ahmad Solihin, said he fled on his motorbike with his wife and two children after a 20-second tremor cracked the walls of his home.
"People suddenly started running so I joined them," he said.
The US Geological Survey said the epicentre was about 52km (32 miles) southwest of the city of Tasikmalaya.