The CVR, which is one of two so-called "black boxes," was buried under eight meters (26 feet) of mud on the ocean floor and was found inside the current search area of 500 to 1,000 meters (546 to 1,093 yards) from the crash site, Navy spokesman Lt. Col. Agung Nugroho told CNN.
He was unable to provide further details on the condition of the CVR. A press conference is expected later Monday.
Aviation expert Geoffrey Thomas said it was an "exceedingly important discovery" and there was no reason authorities should not release the audio or transcripts to the public.
"The Indonesians are very conscious that the whole world is looking at them. I'm sure that the NTSB (National Transportation Safety Board) of the US will put enormous pressure to release it," said Thomas, who is editor-in-chief of AirlineRatings.
The plane's flight data recorder was pulled from the seabed on November 1, but the CVR was detached from it and believed to buried under a thick layer of mud.
The plane, a new Boeing 737 MAX 8, was carrying 181 passengers, six cabin crew members and two pilots. It was heading from Jakarta for Pangkal Pinang on the island of Bangka.
A different flight crew had experienced the same issue on a flight from Denpasar to Jakarta the previous day, but had turned off the automatic safety feature, known as the maneuvering characteristics augmentation system (MCAS) and took manual control of the plane.
The system is new to Boeing's MAX 8 planes and automatically activates to lower the nose to prevent the plane from stalling, based on information sent from its external sensors. Indonesian investigators have already pointed to issues with the plane's angle-of-attack (AoA) sensors, which had proved faulty on earlier flights.
AoA sensors send information to the plane's computers about the angle of the plane's nose relative to the oncoming air to help determine whether the plane is about to stall.
Lion Air's operational director has accused Boeing of withholding information from pilots in the manuals about the feature that automatically lowers the airplane's nose to prevent or exit a stall.
CNN's Ivan Watson and Euan McKirdy contributed to this report.