It is one of the two so-called black boxes. A press conference is expected later Monday.
"It's broken into two pieces so hopefully it's still useful" to investigators, Haryo Satmiko, deputy head of Indonesia's National Transportation Safety Committee (NTSC), told AFP.
The crash, the world's first of a Boeing Co 737 MAX jet and the deadliest of 2018, killed all 189 people on board.
Findings by KNKT now suggest that Lion Air had put the plane back into service despite it having had problems on earlier flights.
They each weigh seven to 10 kg (15 to 22 pounds) and can survive as deep as 6,000m (almost 20,000 feet) underwater or an hour at 1,100 degrees Celsius (2,012 degrees Fahrenheit).
"We don't know what damage there is, it has obvious scratches on it", Nugroho said.
Data from a preliminary investigation report, which didn't state any conclusions, showed the plane's nose pointed down 26 times on its fatal 11-minute flight despite repeated efforts by the pilots to manually aim the nose higher.
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Indonesian authorities said in a statement Monday that the voice recorder was found in Tanjung Kerawang waters in West Java Province.
The cockpit data recorder was recovered within days and showed that the jet's airspeed indicator had malfunctioned on its last four flights.
The flight data recorder gathers information about the speed, altitude and direction of the plane with enough storage for 25 hours of data, while the cockpit voice recorder keeps track of pilots' conversations and other sounds in the cockpit.
Officials, however, warned it could take up to six months to analyse data from the black boxes.
Lion Air is one of Indonesia's youngest airlines but has grown rapidly, flying to dozens of domestic and global destinations.
The pilots appeared to struggle with an automated system created to keep the plane from stalling - a new feature of the Boeing 737 Max.
It has been expanding aggressively in south-east Asia, a fast-growing region of more than 600 million people.