He said Israel also destroyed a Syrian anti-aircraft battery that fired at the Israeli planes, and claimed that Iranian forces are operating less than 80 kilometres from the Israeli border, contrary to Russian assurances.
The official spoke on condition of anonymity under standard Israeli security protocols. The military has not commented on the incident.
Earlier on Wednesday, Russian Defense Ministry spokesman Maj Gen Igor Konashenkov said that six Israeli F-16 jets launched a "provocative" raid at the moment when two civilian airliners were preparing to land in Damascus and Beirut, creating a "direct threat" to the aircraft.
Lebanon's acting Transport Minister Youssef Fenianos later on Wednesday confirmed Konashenkov's account, saying the two airplanes in Lebanese airspace "narrowly" escaped Israeli warplanes, averting a "human catastrophe".
Fenianos said the Lebanese government will present a complaint to the UN Security Council.
The Syrian military didn't fully engage its air defence assets to avoid accidentally hitting the passenger jets, Konashenkov said. He added that Syrian air traffic controllers redirected the Damascus-bound plane to a Russian air base in Syria's coastal province of Latakia.
Konashenkov said the Syrian air defense forces shot down 14 of the 16 precision-guided bombs dropped by the Israeli jets, while the remaining two hit a Syrian military depot 7 kilometres west of Damascus, injuring three Syrian soldiers.
But the Israeli official said all targets had been hit, in some cases causing secondary explosions. He said errant Syrian anti-aircraft fire had endangered the civilian flights.
In recent years, Israel has acknowledged carrying out scores of airstrikes in neighbouring Syria, most believed to have been aimed at suspected Iranian arms shipments to Hezbollah. Iran and Hezbollah have sent forces to Syria to bolster President Bashar Assad, who appears close to victory after a devastating seven-year civil war.
Prime Minister Benjamin Netanyahu has repeatedly said Israel will not allow Iran to establish a permanent military presence in postwar Syria.
That mission has been complicated by the September 17 downing of the Russian reconnaissance aircraft by Syrian fire.
Russia, which also backs Assad, has blamed Israel for the friendly-fire mishap and reportedly scaled back a hotline that allowed the two air forces to coordinate and avoid unintended clashes.