Syria and its main ally Russia blamed Israel for the attack, near the city of Homs, which followed reports of a poison gas attack by President Bashar Assad's forces on the rebel-held town of Douma.
Israel, which has often struck Syrian army locations during its neighbor's seven-year civil war, has neither confirmed nor denied mounting the raid. But Israeli officials said the Tiyas air base was being used by troops from Iran and that Israel would not accept such a presence in Syria of its arch foe.
Iran's Tasnim news agency said seven Iranian military personnel had been killed in the attack, which contributed to a sharp escalation of tensions between the West and Russia.
"(The Tiyas strike) was the first time we attacked live Iranian targets — both facilities and people," New York Times columnist Thomas Friedman quoted the Israeli military source as saying.
Friedman described the seven Iranians killed as members of the Qods Force, a branch of the Iranian Revolutionary Guards Corps that oversees operations abroad, and one of them as a commander of a drone unit.
Asked about the claim of Israeli responsibility cited in the New York Times article, which was published on Sunday, an Israeli military spokeswoman said: "There is no comment at this time."
While acknowledging that it has carried out scores of strikes in Syria against suspect Iranian deployments or arms transfers to Lebanese Hezbollah guerrillas, Israel generally does not comment on specific missions.
The attack on Tiyas came days before the United States, Britain and France launched 105 missiles targeting what Washington said were three chemical weapons facilities in Syria in retaliation for the suspected poison gas attack.
Assad has denied using chemical weapons.
Despite the Israeli source's comment to the New York Times that the killing of Iranians at Tiyas was unprecedented for Israeli missions in Syria, a 2015 air strike there that Hezbollah blamed on Israel killed an Iranian general along with several of the Lebanese guerrillas.