The Boeing 737-500 with 62 passengers and crew was headed on a domestic flight to Pontianak in West Kalimantan on Saturday before it disappeared from radar screens four minutes after take-off.
Indonesia National Transport Safety Committee (KNKT) chief Soerjanto Tjahjono said the locations of Flight SJ 182's two black boxes had been identified.
"Hopefully, we can retrieve them soon," said military chief Hadi Tjahjanto, without giving an estimated timeframe.
Search will continue into the night, a search and rescue official said, but efforts will be limited to sonar scans by boats.
There were no clues yet as to what caused the crash, the first major aircrash in Indonesia since 189 passengers and crew were killed in 2018 when a Lion Air Boeing 737 Max in 2018 also plunged into the Java Sea soon after take-off from Soekarno-Hatta International Airport.
Even before the latest crash, more people had died in air cashes in Indonesia than in any other country over the past decade, according to Aviation Safety Network's database.
Pieces of wreckage were brought to Jakarta port by rescuers, including the plane's altimeter radar, emergency chute and a piece that was suspected to have come off of the bottom part of the plane's tail, KNKT official Nurcahyo Utomo said.
One twisted piece of metal was painted in Sriwijaya Air's blue and red colours. Authorities said they came from a depth of 23 metres (75 feet) near a group of islands off the Jakarta coast.