Ridwan Djamaluddin, a deputy maritime minister, said Monday the National Transportation Safety Committee had informed the ministry about the discovery.
A spokesman for the Indonesian navy's western fleet, Lt. Col. Agung Nugroho, said divers using high-tech "ping locator" equipment had started a new search effort on Friday and found the voice recorder beneath 8 meters (26 feet) of seabed mud.
If the voice recorder is undamaged, it could provide valuable additional information to investigators.
The preliminary crash report from Indonesia's transport safety agency suggested that pilots of Flight 610 struggled to control the plane's anti-stalling system immediately before the crash.
A final crash report is not likely to be filed until later this year.
"This will really help the investigation process. and could give some more answers on the cause" of the crash, said Jakarta-based aviation analyst Dudi Sudibyo.
The main body of the aircraft has never been found.
Officials had said then that it could take up to six months to analyse data from the black boxes.
Indonesia's aviation safety record has improved since its airlines, including national carrier Garuda, were subject to years-long bans from USA and European airspace for safety violations, but the country still recorded more than three dozen fatal accidents over the past 15 years.
Lion Air is one of Indonesia's youngest airlines but has grown rapidly, flying to dozens of domestic and worldwide 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.
Black box data showed the plane also had an airspeed indicator issue on multiple earlier flights.