Israel called it a "severe and irregular violation of Israeli sovereignty" and warned of further action against the unprecedented Iranian aggression.
The military said its planes faced massive anti-aircraft fire from Syria that forced two pilots to abandon an F-16 jet that crashed in northern Israel. One pilot was seriously wounded and the other lightly.
Syrian officials reported large explosions in the center of the country and the Syrian counter fire set off warning sirens throughout northern Israel.
"This is a serious Iranian attack on Israeli territory. Iran is dragging the region into an adventure in which it doesn't know how it will end," Israel's chief military spokesman, Brig Gen Ronen Manelis, said in a special statement.
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"Whoever is responsible for this incident is the one who will pay the price."
Gen Hossein Salami, acting commander of Iran's Revolutionary Guard, did not acknowledge Israel's claim it shot down the drone. "We do not confirm any such news from Israel," he said.
"The Israeli enemy has once again attacked some of our military bases in the southern area and our air defenses responded and foiled the aggression," it said.
Prime Minister Benjamin Netanyahu and Defense Minister Avigdor Lieberman were convening the top brass at military headquarters in Tel Aviv to discuss further response.
Israel has mostly stayed out of the prolonged fighting in Syria, wary of being drawn into a war in which nearly all the parties are hostile toward it.
He said Israel has no interest in further escalation but that it would "extract a heavy price" for such aggression.
He said Iran was "playing with fire" by infiltrating Israeli airspace, and stressed that the unmanned aircraft Israel shot down was "on a military mission sent and operated by Iranian military forces." He said Israel recovered the dispatched drone, which was clearly Iranian.
In response, Conricus said Israeli jets destroyed the Iranian site in central Syria that launched it. Upon their return, the jets came under heavy Syrian anti-aircraft fire.
If the plane was in fact shot down by enemy fire, it could mark the first such instance for Israel since 1982 during the first Lebanon war.
In subsequent attacks, Israel struck four additional Iranian positions and eight Syrian sites in Syria. The military said significant damage was caused.
Conricus said the Israeli jets faced between 15 to 20 anti-aircraft missiles fired by SA-5 and SA-17 batteries. All the Israeli jets in those sorties returned home safely.
The Observatory said the raids resulted in casualties, but didn't specify. It also said Israeli raids targeted areas in southwestern Damascus, bordering the southern provinces. This was followed by raids on Syrian government posts along the Damascus-Beirut road, close to the border between Syria and Lebanon.
Syrian state TV said air defenses hit more than one Israeli plane and that a girl was injured when Israeli missiles fell near a school in a neighborhood in Damascus' countryside.