The cockpit voice recorder, which records conversations between the pilots and with air traffic controllers, was found close to where the flight data recorder was recovered from the bottom of the Java Sea on Monday, the report said.
The Airbus A320-200 airliner lost contact with air traffic control in bad weather on December 28, less than halfway into a two-hour flight from Indonesia's second-biggest city of Surabaya to Singapore. There were no survivors.
The black boxes contain a wealth of data that will be crucial for investigators piecing together the sequence of events that led to the airliner plunging into the sea.
The cockpit voice recorder was now on board an Indonesian navy vessel and expected to be sent to the capital, Jakarta, for analysis, MetroTV said.
Investigators may need up to a month to get a complete reading of the data.
Dozens of Indonesian navy divers took advantage of calmer weather this week to retrieve the black boxes and now hope to find the fuselage of the Airbus.
Forty-eight bodies have been retrieved from the Java Sea and brought to Surabaya for identification. Searchers believe more bodies will be found in the plane's fuselage.