Syrian state news agency Sana said Israeli F-15 aircraft had fired several missiles at the base from Lebanese territory.
The Britain-based Syrian Observatory for Human Rights said it was not clear who was behind Monday's early morning missile strike on the Syrian government's T4 air base.
Syrian state media said they were suspected to be U.S. strikes but the Pentagon formally denied involvement saying it was not conducting air strikes in Syria "at this time".
The strikes reportedly caused an unknown number of deaths.
Israel has previously targeted Iranian units in Syria, but declined to comment on the latest strike.
Syria and Russian Federation have fiercely denounced the allegations of chemical use in Douma as "fabrications", and had warned against using them to justify military action against President Bashar al-Assad.
It took place hours after U.S. President Donald Trump warned of a "big price to pay" following the reports of a poison gas attack on the rebel-held town of Douma which killed dozens of people, including children.
In his tweets Sunday, Trump called Assad an "animal" and delivered a rare personal criticism of Russian President Vladimir Putin for supporting him.
Videos circulated around Arabic-language accounts on Twitter purporting to show either the missiles, or the jets which later fired them, flying above Lebanon.
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The Mongolian capital Ulaanbaatar has also been raised as a possible location, the sources said. Prior to that, Washington had relied mostly on South Korea's assurances of Kim's intentions.
The Observatory gave a higher death toll, saying at least 80 people were killed in Douma, including around 40 who died from suffocation. It was once one of the hubs of the 2011 Arab Spring uprising against Assad's government.
The Syrian American Medical Society and the civil defence service, which operates in rebel-held areas, said 49 people had been killed in the suspected gas attack.
Syria and Russian Federation accused Israel on Monday of carrying out a deadly bombing raid on a Syrian military airport, as calls grew for worldwide action over an alleged chemical attack on a rebel held-town.
Reuters could not independently verify the reports.
The symptoms were consistent with chemical exposure.
For weeks, the remnant rebel holdout east of Damascus has faced an offensive by Syrian government forces, prompting moves to evacuate civilians, although Jaish al-Islam rebels have not confirmed such a deal.
The Organisation for the Prohibition of Chemical Weapons said it had opened an investigation to determine what exactly had happened in Douma. Douma was the only town left holding out.
A 2013 chemical attack in eastern Ghouta that killed hundreds of people was widely blamed on government forces.