"Air defences confronted a huge number of Israeli rockets and some of them achieved their target and destroyed one of the radar websites", Syrian state news agency SANA reported, mentioning a army resource.
Israel had been preparing itself for weeks for possible Iranian retaliation.
The most recent air strikes widely attributed to the Jewish state came on Tuesday, around the time Trump was announcing his withdrawal from the nuclear deal with Iran. The attack appeared to be one of the largest Israel has carried out since it began periodic strikes against Iran and its ally Hizbollah inside of Syria.
Shortly after midnight, IDF defense systems identified approximately 20 rockets that the Iranian Quds forces had launched at IDF forward posts on the Golan Heights.
Israel sees this Iranian attack in a very serious way, "said military spokesman".
Fearing that Iran and Hezbollah are setting up a Lebanese-Syrian front against it, Israel has occasionally struck at their forces.
Iran has also been trying to boost its presence in Syria.
Israel's prime minister said he fully supported Mr Trump's decision, asserting that the deal had "dramatically increased" Iranian "aggression" across the Middle East.
Israel has not commented on the reports, but its government has vowed to stop what it considers Iran's military "entrenchment" in Syria.More news: Microsoft demos phone mirroring and Alexa integration at Build conference
In a speech last May, Trump called for Saudi Arabia to take a leading role in the formation of an anti-Iranian alliance across the region.
Israel clarifies Iran as its biggest threat and Hezbollah while the biggest threat to its own boundaries.
These are the opening skirmishes in what could develop into a brutal war that may sweep across Israel, Lebanon and Syria.
The two countries are still technically at war, although the border remained largely quiet for decades until 2011, when the Syrian conflict broke out.
The war in Yemen, widely seen as a proxy battle between Saudi Arabia and Iran, is another theater Tehran could exploit to inflict pain on its enemies.
"We are trying to avoid at all costs direct military action with Iran, but Iran's behavior such as this can not continue".
The agreement - between Iran and the five permanent members of the United Nations Security Council plus Germany - imposed curbs on Iranian nuclear activities in return for the lifting of worldwide sanctions.
It came as President Donald Trump said the United States would quit the Iran nuclear deal.
In 2011, USA officials said they foiled an Iranian plot to assassinate Saudi Arabia's ambassador to the United States, Adel al-Jubeir, the current Saudi foreign minister.