Israel has long targeted Iran's military installations in Syria and those of its proxies, but Monday's attack was the first time it apparently hit the vast embassy compound itself.
The Kremlin said that the suspected Israeli attack is an act of aggression and a "violation of all the foundations of international law."
Iran vows to take revenge on Israel for Damascus airstrike as the US tells Iran it 'had no involvement' in airstrike.
Two civilians injured in alleged Israeli strikes in the outskirts on Damascus.
Earlier on Thursday, a site used by the IRGC in Sayyida Zeinab near Damascus was targeted in an alleged Israeli airstrike.
This was the second time within 48 hours that the same area was targeted by alleged Israeli airstrikes.
Sky News Arabic reported that the alleged targets of the missile strike were Iranians.
This comes as Israel and the United States have stepped up strikes on Iranian and Iran-aligned targets.
The strikes come just days after alleged Israeli airstrikes targeted sites in Homs in central Syria.
Syrian state media said only material damage was caused by the airstrikes.