A navy diver told broadcaster Metro TV on board a search vessel his team found the orange-colored box intact in debris on the muddy seafloor.
Indonesia’s transportation safety committee (KNKT) will analyze its data in Jakarta, which could take up to two weeks.
Searchers have yet to find the second black box containing recordings of cockpit conversations. Strong currents have hampered search efforts, complicated by the presence of energy pipelines in the area.
The discovery of the black box may provide some relief to grieving relatives. But hopes are fading of finding a large section of fuselage intact with bodies, easily retrievable, inside.
The commander of the navy divers involved in the search was quoted by the Kompas.com news portal as saying divers had found many bodies. But only one has been identified.
“What is important for us is to get more information about the victims because having their remains back is important for us so we can bury them properly,” said Ade Inyo, whose brother in law was on the flight.
President Joko Widodo has also ordered a review of all regulations relating to flight safety.
Indonesia is one of the world’s fastest-growing aviation markets. Its transportation safety committee investigated 137 serious aviation incidents from 2012 to 2017.
Lion Air said the aircraft that crashed had been airworthy and the pilot and co-pilot had 11,000 hours of flying time between them.
But according to the transport safety committee, the plane had technical problems on its previous flight on Sunday, from the city of Denpasar on the resort island of Bali, including an issue over “unreliable airspeed”.
Lion Air chief executive Edward Sirait has acknowledged reports of technical problems with the aircraft, but said maintenance had been carried out “according to procedure” before it was cleared to fly again.
Lion Air’s only other fatal accident was in 2004 when an MD-82 crashed upon landing at Solo City, killing 25 of the 163 people on board, according to the Flight Safety Foundation’s Aviation Safety Network.