SANA added that material damage had been sustained in the strikes as well and that the main international airport in the capital was temporarily out of service as a result of the damage sustained.
The transport ministry said in an online statement that workers had removed debris from the strikes and that flights would resume by 9 a.m.
Reuters cited regional intelligence sources as saying that the strikes hit an outpost controlled by Iran's Quds Force and associated militias.
The Syrian army said on Monday that Israel had carried out a missile strike on Damascus International Airport and put it out of service, the latest in a string of alleged Israeli strikes targeting Iran-linked assets.
A volley of air-launched missiles had hit the airport at 2 a.m., the army said in a statement, adding that missiles also hit targets in the south of Damascus, killing two members of the Syrian armed forces and causing some damage.
Earlier, two regional intelligence sources said the strikes had hit an outpost near the airport of Iran's Quds Force and the militias it backs. Their presence has spread in Syria in recent years.
Previous alleged Israeli airstrikes in Syria
In June of this year, flights in and out of Damascus International Airport were halted for two weeks after alleged Israeli strikes caused extensive damage to infrastructure, including a runway and a terminal.
Then, on October 21, Syria again accused Israel of carrying out a missile strike against Damascus and the country’s southern region after just over a month with no missile strikes.
At the time, reports said the target of the attack was the Damascus International Airport, which has been struck by Israel repeatedly as part of MABAM, its war-between-wars campaign against Iran’s attempt to entrench itself in the country and smuggle weapons to Hezbollah in Lebanon.
In addition to the Damascus airport, Israel has also allegedly struck Aleppo International Airport in recent months.
Western and regional intelligence sources say Tehran has adopted civilian air transportation as a more reliable means of ferrying military equipment to its forces and to allied fighters in Syria, following alleged Israeli disruption of ground supply.