Israel launched a series of predawn air strikes then followed up with artillery fire on an army base near the Syrian capital, Damascus, Syria's military said.
The allegation was not denied by Israeli Prime Minister Benjamin Netanyahu when questioned by reporters later on Tuesday.
Israeli jets fired missiles at the Qutayfeh area northeast of Damascus from inside Lebanese airspace at 2:40am local time (00:40 GMT), causing the Syrian army to retaliate and "hit one of its planes", the Syrian army said in a statement broadcast on state television.
UK-based war monitor, the Syrian Observatory for Human Rights, said the air strikes targeted Syrian army and Hezbollah weapons depots, igniting "successive explosions and fires, causing material damage".
After the air raids, Israel also launched rockets from the occupied Golan Heights, but the Syrian military intercepted them, the army statement said.