According to state-run SANA, "Syrian air forces intercepted an Israeli aggression and downed a number of missiles which were targeting T-4 airport in Homs".
Russian officials had no immediate comment on the meeting.
"And I would like to point out that we will be preventing any attempts to violate our air or land border", Netanyahu said as he met Putin.
Israel will not dismiss the possibility of future relations with Syrian President Bashar al-Assad, Defence Minister Avigdor Lieberman said on Tuesday.
The patients, Israeli medical officials said, were not the walking wounded of the seven-year-old Syrian civil war but children with chronic health problems coming across the frontier for a day's treatment in a hospital in northern Israel.
Israel shot down the drone.
Israel is particularly anxious about the presence of Damascus ally Iran next door in Syria. Russian Federation has been a key ally of Syrian President Bashar Assad in the Syrian civil war and its forces on the ground have managed to turn the tide in Assad's favor in recent years.
Israel's Ambassador to the United Nations, Danny Danon, called on the U.N. Security Council to condemn Wednesday's drone incident as a "dangerous act that not only threatens Israel, but the stability of the entire region".
Russian Defense Minister Sergei Shoigu said Moscow is ready to discuss the issue of supplying Syria with the S-300 missile system.
"At the meeting (with Putin), the prime minister will make clear that Israel will not tolerate military entrenchment by Iran or its proxies anywhere in Syria, and that Syria must abide meticulously by the 1974 separation agreement", an official Israeli statement said.
Lieberman has also stepped up rhetoric against the Syrian military warning them not to enter a buffer zone in the Syrian Golan Heights established after a 1973 war with Israel.