"We intercepted it and we will continue to act decisively against any spillover and any infiltration of Israeli territory or airspace".
The Israel military has said it fired a Patriot missile at a drone coming from Syria.
On Tuesday, Netanyahu met with Russian envoys Alexander Lavrentiev and Deputy Foreign Minister Sergey Vershinin, in Jerusalem, reiterating again Israel's objection to an Iranian presence in Syria.
"The aircraft of the Israeli enemy launches a number of missiles at several army positions" in the southwestern province of Quneitra, causing material damage, it said.
Shortly afterward, Netanyahu held a lengthy meeting with Putin in which they established a joint Israeli-Russian team to coordinate military activities and mitigate "misunderstandings".
On Sunday, Syria accused Israel of attacking an air force base near Homs that was known to be housing Iranian forces.
The alarms sounded in the Golan Heights and the Jordan Valley were triggered by the unmanned aerial vehicle's violation of Israeli air space.
Russia, another top key ally of Assad, has warned it would be unrealistic to expect Iran to fully withdraw from the country. In the past, Putin has turned a blind eye to Israeli strikes on Iranian and Hezbollah targets in Syria while making clear Moscow does not want Assad's rule endangered.
"We made a decision to bring with us two wonderful children who are bravely fighting cancer: Mika, whom my wife and I have known for nine years, and Alon, whose parents emigrated from Russian Federation and who likes soccer very much".
Israel has signaled openness to eventual ties with Assad, a tacit acknowledgement that he is re-consolidating power as he routs Syria's rebels.
Netanyahu's government has made clear it would not cede the Golan now and has been lobbying for United States recognition of Israel's claim of sovereignty there.