The Israeli military spokesman said the Iranian attack with around 20 projectiles or rockets was carried out by the Quds Force, an external arm of Iran's Revolutionary Guards.
Lieutenant Colonel Jonathan Conricus said that Israel intercepted "a few" of the rockets and there were no reports of casualties and that damage to Israeli positions was "limited."
The attack took place at around 12.10 a.m. "We have retaliated but I have no further details about this," he said.
Tensions between Israel and Iran had already spilled over in Syria. Iran vowed retaliation after an Israeli air strike last month killed seven of its military personnel in a desert airbase in Syria. Israel regards Iran as its biggest threat, and has repeatedly targeted Iranian forces and allied militia in Syria.
Syrian state media reported Israeli missile attacks targeting Baath City in Quneitra, near the border. Further waves of missiles followed. Syrian state media said Israeli missiles had been brought down over Damascus, Homs and Sueida.
"Air defences confronted tens of Israeli rockets and some of them reached their target and destroyed one of the radar sites," Syrian state news agency SANA reported, citing a military source. Another rocket hit an ammunition warehouse, it said.
Asked whether Israel had attacked near Damascus or scrambled communications there, an Israeli military spokeswoman said: "I have no comment on that at this time."
Syrian state television was broadcasting footage of its air defenses firing, and playing patriotic songs. Damascus residents described explosions in the sky from air defense systems.
Israeli media said residents of Metulla, on the Lebanese border, had been instructed to go to bomb shelters. There was no official confirmation.
Lebanon's National News Agency, citing Lebanese Army Command, reported Israeli jets circling over Lebanese territory early on Thursday before exiting.