The confrontation was the most serious between arch foes Israel and Iran since the start of the civil war in Syria in 2011.
Israel's raids came after it intercepted what it said was an Iranian drone entering its airspace from Syria, which it labelled an "attack."
It marked the first time Israel publicly acknowledged attacking what it identified as Iranian targets in Syria since the war began.
Israeli military spokesman Jonathan Conricus warned that Syria and Iran were "playing with fire," but stressed that his country was not seeking an escalation.
"This is the most blatant and severe Iranian violation of Israeli sovereignty in the last years," Conricus told journalists in a phone conference.
"That's why our response is as severe as it is."
Israel said its reprisals after the exchange were "large-scale" raids that attacked Syrian air defence systems and Iranian targets.
"Twelve targets, including three aerial defence batteries and four Iranian targets that are part of Iran's military establishment in Syria were attacked," a military statement said.
Israel has repeatedly warned in recent weeks against the presence of Iranian forces in neighbouring Syria.
'Iran is responsible'
The Israeli pilots of the crashed F16 were reported alive, although one was severely wounded.
According to the Israeli military, the confrontation began with the drone entering its airspace.
Israeli forces identified an "Iranian UAV (unmanned aerial vehicle)" launched from Syria and intercepted it in Israeli airspace with a combat helicopter, a statement said.
Conricus said it was intercepted well inside Israeli territory over the city of Beit Shean, near the Jordanian border.
He did not say whether the drone was armed or strictly for reconnaissance, but said: "We know it was on a military mission sent by Iranian military forces."
Israeli aircraft then "targeted the Iranian control systems in Syria that sent the UAV into Israeli airspace," according to Conricus.
The aircraft met "massive Syrian anti-air fire," Conricus said, and the F16 crashed afterwards in the Jezreel valley in northern Israel.
It was not clear if the jet crashed as a direct result of the Syrian fire.
According to a separate military statement, "multiple anti-aircraft missiles were fired at IAF (Israel Air Force) aircraft."
"The pilots of one of the aircraft abandoned as per procedure. The pilots landed in Israeli territory and were taken to the hospital for medical treatment."
Conricus said the army had confirmed "accurate hits of (the) Iranian UAV control facility" in Syria.
"Iran is responsible for this severe violation of Israeli sovereignty," Conricus said on Twitter.
Syria said its air defences repelled two Israeli raids on its military bases in the centre of the country, hitting more than one warplane during the first.
"At dawn, the Zionist enemy carried out a new aggression against one of our military bases in the centre of the country," state news agency SANA reported.
"Our air defences repelled it and hit more than one plane."
'Nobody tries us'
The Syrian Observatory for Human Rights, a Britain-based monitor of the seven-year civil war, said the earlier Israeli raids had targeted several military bases in the east of the central province of Homs.
It said the bases are used by both Iranian and Russian military personnel deployed in support of the regime.
Syrian state media said the later raids targeted military positions in the south of the country.
Air raid sirens had gone off in Israel in the early hours of the morning following the UAV interception and raids.
The army said it was "monitoring events and is fully prepared for further action, depending on assessments and necessity."
Israeli Prime Minister Benjamin Netanyahu has held a series of meetings in recent months with Russian President Vladimir Putin on Iran's influence in war-torn Syria and Lebanon.
Netanyahu has been seeking to persuade Russia to limit Iran's presence near Israeli territory and to stop it from entrenching itself militarily in Syria.
Russia, Iran and Lebanon's Shiite Muslim militant group Hezbollah -- which is backed by Tehran -- all support Syrian President Bashar al-Assad in the civil war.
In a meeting in Moscow last month, Netanyahu reiterated Israel's concerns of what he described as the attempts of Iran to establish a military presence in Syria and produce accurate weapons against Israel there.
"We won't accept either of those, and will act according to our needs," Netanyahu said following the meeting with Putin.
Israel remains technically at war with Syria and occupies a swathe of the strategic Golan Heights that it seized in the Six-Day War of 1967 and later annexed in a move never recognised by the international community.
On Tuesday, Netanyahu took members of his security cabinet for a tour of the Israeli-occupied side, where they were briefed by the military on the situation.
"We want peace, but are prepared for any scenario, and suggest that nobody tries us," he said.
Israel has sought to avoid direct involvement in the Syrian war, but acknowledges carrying out dozens of air strikes there to stop what it says are advanced arms deliveries to Hezbollah
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)