He said: "Video shows Missile launched against unknown Target in Far East Damascus countryside".
Most of the missiles were downed, a Syrian military official said.
The Pentagon on Monday denied any involvement in an attack on a Syrian air base outside Homs, not far from where USA, United Kingdom and French missiles struck early Saturday morning.
Asked about the missile attack, an Israeli military spokesman told Reuters, "We don't comment on such reports".
Damascus skies erupt with surface to air missile fire as the U.S. launches an attack on Syria targeting different parts of the Syrian capital Damascus, Syria, April 14, 2018.
Near Damascus, the pro-regime media reported that three missiles had been launched at the Damir airbase close to the capital.
Initial reports claim the raid is aimed at the T4 base, but others say it is aimed at Shyrat AB which was hit past year in the US Tomahawk attack.
According to yet unconfirmed reports, the missiles entered Syrian airspace from Lebanon, which may indicate that the Israeli Air Force could have been involved, Al-Masdar News reports, citing a military source.
There are now no reports of targets hit in Damascus.
Syrian air defense systems have been activated in response to a missile attack apparently targeting Shayrat Airbase in Homs province, state media SANA reports.
The Pentagon has declared there is "no U.S. military activity near Homs at this time".
The strike was created to disable the country's use of chemical weapons after it allegedly used chlorine against rebels in Douma, eastern Ghouta on April 7.