Tehran said the strike killed seven military advisers, including three senior commanders.
The target, according to Iranian state media, was top Revolutionary Guards commander Mohammad Reza Zahedi.
He had been a senior commander in Iran's elite Quds Force - the corps' overseas arm - according to the Guards.
Iran's Ambassador to Syria Hossein Akbari said Tehran's response would be "harsh."
Syria's foreign minister condemned the attack.
Its state media cited a military source saying Israel launched the attack from the occupied Golan Heights and that its air defense system shot down some of the missiles.
The strike appeared to signal an escalation in Israel's war against Iran's regional proxies.
Israel has long targeted Iranian military installations in Syria, as well as the proxies.
Monday's attack marked the first time Iran's embassy compound itself had been hit.
Since the attack on Israel nearly six months ago by Palestinian group Hamas, which is also backed by Iran...
Israel has also ramped up strikes in Syria against Iran's Guards, as well as Hezbollah, the Tehran-backed Lebanese armed group.
They both support Syria's government of President Bashar al-Assad.
The White House said it was still looking into reports about the strikes...
While State Department spokesperson Matthew Miller said the goal is still to prevent any possible escalation of conflict:
"We are always concerned about anything that would be escalatory or cause an increase in conflict in the region."
Israel typically does not comment on its attacks in Syria, and declined to do so on Monday.
Although it also said on Monday it had stopped weapons from being smuggled into the West Bank from Iran.
