The Boeing 737 crashed on 25 January, minutes after take-off from Beirut airport during a fierce thunderstorm, killing all 90 people on board.
An army official said the recorder was taken to a naval base in Beirut to be handed over to crash investigators.
The search continues for the cockpit voice recorder and 75 missing bodies.
Passenger jets carry two recorders – a flight data recorder and a cockpit voice recorder – commonly referred to as “black boxes”.
Lebanon’s Transport Minister, Ghazi Aridi, said he hoped the voice recorder and the missing bodies would be recovered soon.
The recorders will be sent to France’s accident investigation agency BEA, he told the AFP news agency.
Mr Aridi announced on Saturday that searchers had located the recorder at a depth of 150ft (45m) off the coastal village of Naameh, just south of Beirut airport.
Since then, searchers had also located the plane’s rear wings and cockpit, and work was continuing to bring them to the surface, he said.
The cause of the crash is not yet known. Lebanese officials have said the jet did not fly in the direction instructed by the Beirut control tower.
The recorder could shed light on why the pilot failed to respond to the control tower’s request, even though he acknowledged their commands.
A technical committee composed of Lebanese, Ethiopian and French experts is charged with investigating the crash.
Seven crew and 83 passengers were on board the Boeing 737-800. Most were Lebanese or Ethiopian.
Only 15 bodies have been recovered since the crash, but stormy weather has hampered searchers.