The state broadcaster earlier said explosions were heard at the T-4 airfield near Homs, which is close to the ancient city of Palmyra in central Syria.
According to the Syrian Observatory for Human Rights (OSDH), at least 14 military personnel, including Iranians, were among those killed in the strike that took place shortly before dawn.
A Syrian military source was quoted as saying air defences shot down eight missiles fired at the base, also known as the Tiyas Airbase, where defence analysts say there are large deployments of Russian forces, and where jets fly regular sorties to strike rebel-held areas.
The state broadcaster said there were several dead and wounded in the strike.
The base is in a strategic desert area, where Syria's main gas fields are located. It had been under the control of Islamic State militants until the Syrian army and its allies regained control last year after heavy Russian military intervention.
"An aggression was perpetrated on T-4 air base in several strikes that is most likely to be an American attack," state television said in a news flash.
The US Pentagon said it was not conducting air strikes in Syria "at this time," formally denying the Syrian state television report.
When asked about the explosions, an Israeli spokeswoman declined to comment.
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.
An intelligence source based in the region told Reuters he did not rule out an Israeli strike on the base.
Israel had previously said Syria had allowed Iran to set up a complex at the base to supply its ally, the Lebanese militant Shi'ite group Hezbollah, with weapons.
The Israeli military last February accused Iranian-backed militias of operating at the base, from where it said an Iranian drone, that was shot down over northern Israel, had been launched.
Israel has long said Iran was expanding its influence in a belt of territory that stretches from the Iraqi border to the Lebanese border, where Israel says Iran supplies Hezbollah with arms.
Hezbollah and other Iranian-backed militias have a large military presence in Syria and are well entrenched in central and eastern areas near the Iraqi border.
US President Donald Trump said earlier on Sunday there would be a "big price to pay" after medical aid groups reported dozens of civilians, including many children and women, were killed by poison gas in a besieged rebel-held town.
The United States launched a cruise missile strike on a Syrian air base a year ago in response to the killing of dozens of civilians in a sarin gas attack in an opposition-held town in northwest Syria. The gas attack was blamed on Assad.
The US missile strike was against a Syrian air base which Washington said was used to launch the strike.
The Syrian state denied government forces had launched any chemical attack. Russia, President Bashar al-Assad's most powerful ally, called the reports fake.
AFP contributed to this report.