Syrian state television quoted the army as saying several rockets were fired from an area near Lake Tiberias in northern Israel just after midnight which landed in the compound of the airport, a major facility for elite Republican Guards.
"Syrian army command and armed forces warn Israel of the repercussions of the flagrant attack and stresses its continued fight against (this) terrorism and amputate the arms of the perpetrators," the army command said in a statement.
The statement did not disclose if there were any casualties, but said the rockets caused a fire.
Video footage downloaded on social media showed large volleys of fire engulfing several areas in the military airport's compound with a huge plume of smoke from the airport area seen from a distance in several neighborhoods of the capital.
Earlier, state television said several major explosions hit Mezzah military airport compound near Damascus and ambulances were rushed to the area, without giving details.
The airport, located southwest of the capital, had been a base used to fire rockets at former rebel-held areas in the suburbs of Damascus.
Israel in the past has targeted positions of Lebanon's powerful Hezbollah group inside Syria where the Iranian-backed group is heavily involved in fighting alongside the Syrian army.
An air strike in Syria in December 2015 killed Hezbollah prominent leader Samir Qantar, with Israel welcoming his death, saying he was preparing attacks on it from Syrian soil, but stopping short of confirming responsibility for his death.
Earlier that year, an Israeli air strike in Syria killed six members of Hezbollah, including a commander and the son of the its late military chief Imad Moughniyah near the Golan Heights.
Israeli defense officials have voiced concern that Hezbollah's experience in the Syrian civil war, where it has played a significant role and recently helped the Syrian army regain the eastern sector of the city of Aleppo, has strengthened it.
Rebels operating in the area have said Hezbollah's major arms supply route into Damascus from the Lebanese border has been targeted on several occasions in recent years by air strikes. This has included strikes on convoys of weapons and warehouses.
Damascus airport was also hit by air strikes in 2013. Tel Aviv neither confirms nor denies involvement in striking targets inside Syria.
(Reporting by Suleiman Al-Khalidi; Editing by Cynthia Osterman and Leslie Adler)
