It said weapons storage, logistics sites and intelligence centres were among the targets.
Explosions were heard in the capital Damascus before dawn and air defence systems were heard throughout the night.
The strikes are the country’s most significant military action in neighbouring Syria since the war started in 2011.
It was in response to attacks on the Golan Heights – an Israeli-controlled Syrian territory – in the early hours of Thursday, during which residents sought safety in bomb shelters.
Israeli military spokesman Lieutenant Colonel Jonathan Conricus said later that damage to Israeli positions was “limited”.
He said on Twitter: “Iranian Quds force fired 20 rockets towards forward IDF (Israeli Defence Force) positions on Golan Heights.
“Several rockets intercepted. No Israeli casualties.
“The IDF views this Iranian attack with severity.”
The pro-Syrian government Al-Mayadeen TV said more than 50 missiles had been fired at Israeli forces.
The attacks are the latest in a tense exchange between the two enemies, with Iran blaming Israel for a 9 April fatal airstrike on Iranian positions in Syria.
Iran has also been trying to boost its presence in Syria.
It is a key ally of President Bashar al-Assad and its Hezbollah forces have been helping beat back a seven-year rebellion against him.
Earlier on Wednesday, Israeli Prime Minister Benjamin Netanyahu arrived in Moscow for talks with Russian President Vladimir Putin on military coordination.
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Adding to the tensions in the region, US President Donald Trump announced on Tuesday that his country would withdraw from the 2015 nuclear deal with Iran.
That move prompted Iran’s Supreme Leader, Ayatollah Ali Khamenei, to say that Mr Trump’s body “will be food for worms”.