Ridwan Djamaluddin, a deputy maritime minister, told reporters on Monday that the National Transportation Safety Committee (KNKT) had informed the ministry about the discovery.
He added that human remains were also discovered at the seabed location.
Separately, Reuters news agency quoted Haryo Satmiko, KNTK deputy chief of Indonesia's transport safety committee, as saying: "It's been found, but we have not received information of the location yet."
The cockpit voice recorder is one of the two so-called black boxes crucial for the investigation of a plane crash.
The two-month-old Boeing 737 MAX 8 jet plunged into the Java Sea just minutes after taking off from the capital, Jakarta, on October 29.
It was the the world's first of a Boeing Co 737 MAX jet.