The report did not indicate who might have fired the missiles over the Homs region, which Syrian state television called an act of "aggression".
The United States a year ago targeted the Shayrat airbase with cruise missiles in response to a sarin gas attack on the rebel-held town of Khan Sheikhun.
Syrian state media is widely believed to exaggerate their claims of shooting down incoming missiles.
The Syrian Observatory for Human Rights, a UK-based war monitor, reported that big explosions were heard near Shayrat airbase and two other airbases near Damascus.
Asked about the missile attack, an Israeli military spokesman told Reuters, "We don't comment on such reports".
Following reports of an Israeli strike, an Israeli military spokesman said: "I'm not aware of such an incident".
Hezbollah's AlManar TV reported that six missiles targeted Shayrat and three were aimed at Dumair military airport outside Homs on Monday.
Site of previous USA attack: The Shayrat airbase was the target of an April 2017 U.S. missile attack in response to an earlier chemical weapons attack by the Syrian government.
According to the Pentagon, US intelligence had established that the base was the launchpad for the alleged chemical attack.
Israel has struck Syrian army locations many times in the course of the conflict, hitting convoys and bases of Iranian-backed militias that fight alongside Syrian President Bashar al Assad's forces.