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 Guar.
"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.
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.
Israeli defence 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.
Seven killed in suicide attack
Earlier, a powerful blast caused by a suicide bomber has hit a heavily policed district of the Syrian capital of Damascus with at least seven killed, a police source told state television.
The source says the bomber blew himself in the Kafr Sousa neighbourhood where some of Syria's main security installations are located.
The British-based Syrian Observatory for Human Rights which tracks violence across the country said the death toll was expected to rise with several of the wounded in a critical condition.
Footage on state media showed splattered blood and wreckage of several cars with dozens of heavily armed security personnel at the site of the explosion.
Last July a car bomb also hit Kafr Sousa near an Iranian school in an attack that killed several people in the area, close to the main Umayyad Square that connects the city with several highways.
Insurgents fighting to topple President Bashar al Assad say the district houses many recruits from Iranian-backed militias fighting alongside the army.
