The IDF announcement came moments before President Donald Trump announced the USA was pulling out of the global deal to limit Iran's nuclear weapons program. Photos on social media appeared to show fires in al-Kiswah, an industrial area home to an army base, after it was hit.
The station on Tuesday night quoted the military as saying that the Syrian air defenses made the interceptions on the outskirts of the capital Damascus.
Israel has not yet commented on the report.
Israel's military, however, said Tuesday its forces were on high alert near its border with Syria after spotting Iranian activity and was urging civilians in the Golan Heights near Syria to prepare bomb shelters.
In Washington, CNN reported on Tuesday that United States defence officials are seeing signs that Iran is preparing to strike Israel, possibly from Syria.
Iran blamed Israel and vowed to retaliate. On Tuesday, the Israeli army ordered the opening and preparation of missile shelters in the occupied Golan Heights, but stopped short of instructing residents to occupy the shelters. "The IDF is prepared for various scenarios and warns that any aggression against Israel will be met with a severe response".
The U.S. Embassy in Israel also issued an advisory to its government employees, barring them from visiting Israel's northern region without first securing approval.
Israeli officials have confirmed the Jewish state has carried out dozens of attacks in recent years on convoys of Iranian weapons being sent through Syria to Hezbollah, Iran's proxy militia in Lebanon.