Syria's official news agency SANA said "the Israeli attack targeted the Iranian consulate building in the Mazzeh neighbourhood of Damascus".
There was no immediate comment from Israel, which has stepped up strikes on Iran-linked militant groups amid its Gaza war raging against Hamas since October 7.
AFP correspondents at the site confirmed the building next to the embassy, an annex, had been levelled, in an upscale neighbourhood of Damascus.
Iranian media also reported that the strikes in Damascus completely destroyed the annex building, and that the ambassador was unharmed.
"Hossein Akbari, ambassador of the Islamic Republic of Iran in Damascus, and his family were not harmed in the Israeli attack," Iran's Nour news agency said.
Two AFP correspondents at the site confirmed the building next to the embassy, had been razed to the ground by the strike.
Britain-based group the Syrian Observatory for Human Rights said "Israeli missiles... destroyed the building of an annex to the Iranian embassy... in Damascus, killing six people".
Syria's official SANA news agency earlier reported that "our air defence systems confronted enemy targets in the vicinity of Damascus".
The incident came days after the Observatory reported Israeli strikes that killed 53 people in Syria, including 38 soldiers and seven members of the Iran-backed Hezbollah.
It was the highest Syrian army toll in Israeli strikes since the Israel-Hamas war began on October 7, said the monitor.
