The reports said the missiles had targeted Shayrat airbase in Homs province and Dumair military airport, northeast of Damascus, late on Monday night.
State TV said the country’s air defences had confronted a new “aggression” but gave no further details.
It is unclear who was behind the attack but America said its military was not involved.
Dumair is used by Syria’s military to support the campaign against rebels in eastern Ghouta.
It comes just days after the UK, US and France launched airstrikes on three targets following the latest alleged chemical attack by the Syrian regime in Douma.
But US Pentagon spokeswoman Heather Babb said: “There are no US or coalition operations in that area.”
There has been speculation that Israel launched the strikes.
An Israeli military spokesman said: “We don’t comment on such reports.”
Israel’s main concern in Syria is the growing influence of Iran, which it says supplies weapons to Hezbollah from inside the country.
Israel has struck Syrian military targets before and was blamed for strikes earlier this month on the T4 air base in Homs.
That attack killed four Iranian military personnel – but Israel did not confirm or deny involvement.
More from Israel
‘Spelling error’ gets banned Dublin mayor Michael Mac Donncha into Israel
Photographer dies covering Israel-Gaza border protests
Gaza hospitals discharging seriously injured patients to make room ahead of border protests
Eighteen Palestinians confirmed killed in Gaza border protests
UN calls for investigation on Gaza clashes after 16 killed
US ambassador to Israel is ‘son of a dog’, says Palestinian president Mahmoud Abbas
Moscow and Damascus claimed two Israeli fighter planes carried out that airstrike “remotely from Lebanese territory”.
Russian foreign minister Sergei Lavrov described it as a “provocation” and a “very dangerous development”.