The ferry Levina 1, heading for Bangka island off the coast of Sumatra, was carrying about 350 passengers, naval officials said.
Colonel Didin Z A, who heads the navy rescue team, said that the dead included at least three children.
Lieutenant-Colonel Hendra Pakan of the Indonesian navy's western fleet, said at least 211 passengers and crew were rescued.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Pakan said that a navy ship had reported the vessel was still on fire, contradicting an earlier official who said that the blaze had been put out.
"It looks like the fire has got bigger," he said.
"We are still looking for (anyone unaccounted for) by combing through the waters. They may have jumped into the sea because the ferry was hot due to the fire," Pakan added.
The blaze is the latest in a series of incidents to hit Indonesia's transport sector.
In late December a ferry travelling from Indonesian Borneo to the main island of Java sank in high seas with some 600 passengers on board.
About 250 passengers were found clinging to life-rafts - many several days later - but the rest are thought to have drowned.
Just days after the sinking an airliner belonging to Indonesian budget carrier Adam Air disappeared from radar near the island of Sulawesi.
After an intense search small pieces of debris from the aircraft were eventually found by local fishermen, but no remains of the 101 passengers and crew have yet been recovered.
Ferries are a popular means of transport among Indonesia's 17,000
islands, where sea connections are cheaper and more available than air routes.
But safety standards are often not strictly enforced and many ferries are overcrowded.