"The device was damaged and the retrieval process was conducted in several stages," the committee said in a statement.
It said a vessel used equipment to pick up the memory unit, which is considered the recorder's most important part.
The Airbus A320, which had 66 people aboard, crashed May 19 in the Mediterranean Sea on a flight from Paris to Cairo. Authorities have been searching for wreckage and the plane's flight data and cockpit voice recorders for insight into what happened.
The cockpit voice recorder is one of the so-called black boxes for which searchers have been looking. It captures sounds on the flight deck that can include conversations between pilots, warning alarms from the aircraft and background noise. By listening to the ambient sounds in a cockpit before a crash, experts can determine if a stall took place and estimate the speed at which the plane was traveling.
The recorder is being transferred to Alexandria, Egypt, for the investigation, the statement said.
The wreckage the government said it found Wednesday had been strewn across several places. Officials did not specify the size or the location of the parts.
Searching for other 'black box'
Searchers haven't found the other "black box," the flight data recorder, which gathers 25 hours of technical data from the airplane's sensors, recording several thousand distinct pieces of information. Among the details investigators could uncover is information about the plane's air speed, altitude, engine performance and wing positions.
Two weeks ago, a French naval vessel detected underwater signals from one of Flight 804's black boxes
, investigators said.
Specialized locator equipment on board the French vessel La Place detected signals from the seabed in the Mediterranean, the investigative committee said.
The director of the BEA, France's air accident investigation agency, later confirmed the signals were from one of the plane's recorders.
"The signal of a beacon from a flight recorder could be detected. ... The detection of this signal is a first step," said BEA Director Remy Jouty in a statement.
The John Lethbridge, a vessel contracted by Egypt for the search, recovered the cockpit voice recorder.
Once the other black box is found, it will be brought to Egypt, a civil aviation ministry official told CNN. That standard procedure, the official said, is similar to what happened in November with recorders from Metrojet Flight 9268, which crashed in Egypt's Sinai Peninsula.
Data recorders have been fixtures on commercial flights around the world for decades.
In several cases -- such as the 1996 crash of TWA Flight 800 or the crash of American Airlines Flight 77 on September 11, 2001 -- authorities had hoped to find clues in the recorders, only to discover that the data inside had been damaged or the recordings had stopped suddenly.