Israel's military said on Monday it struck Iranian Quds targets inside Syria and warned Syrian forces not to attack Israeli territory or forces, Reuters reports.
Syrian state media cited a Syrian military source as saying Israel launched an "intense attack through consecutive waves of guided missiles", but that Syrian air defences destroyed most of the "hostile targets".
Witnesses in Damascus said loud explosions rang out in the night sky for nearly an hour.
"We have started striking Iranian Quds targets in Syrian territory. We warn the Syrian Armed Forces against attempting to harm Israeli forces or territory," Israel's military said in a statement.
The Quds Force is in charge of Iran's Revolutionary Guards' overseas operations.
The strikes followed cross-border attacks on Sunday in which Syria said it repelled an Israeli air attack. Israel said it intercepted a rocket fired at the Golan Heights.
"We have a permanent policy, to strike at the Iranian entrenchment in Syria and hurt whoever tries to hurt us," Israeli Prime Minister Benjamin Netanyahu said earlier.
The Israeli army said a popular winter sports site on Mount Hermon in the Israeli-controlled Golan Heights would be shut for the day. It added that otherwise, things remained "routine" along the frontier with Syria.
Netanyahu last week acknowledged an Israeli attack on what he called an Iranian arms cache in Syria, where Tehran provides Damascus with vital support.
He told his cabinet Israel had carried out "hundreds" of attacks over the past years of Syria's war to curtail Iran and its ally Lebanon's Hezbollah.
Usually silent about its attacks on Iranian targets near its frontier, Israel has lifted the veil this month, a sign of confidence in a campaign waged amid occasional tensions with Syria's big-power backer Russia.