State TV quoted a military official as saying that Israel fired missiles from the direction of the Israeli-occupied Golan Heights at military positions near the capital.
The official news agency Sana one soldier was wounded in the attack that caused “material damage".
The Syrian Observatory for Human Rights, an opposition war monitor, said two pro-regime fighters were killed in the attack, south-west and south-east of the capital.
"Israeli missiles destroyed arms depots of pro-Iran militias and the Lebanese Hezbollah a few kilometres from the Damascus International Airport and around the Kiswah area," it said.
Israel has launched hundreds of air strikes on Syrian territory since the civil war began in 2011. Most of the strikes have targeted Iran-backed militias supporting the government and fighters from Hezbollah. It has also targeted airports in Damascus and the northern Syrian city of Aleppo.
Israel rarely comments on such air strikes but has repeatedly said it will not allow its arch-foe Iran to expand its presence in the country.
Iran and Russia have been the main backers of Syrian President Bashar Al Assad in suppressing the armed uprising against his rule, leaving the north-western Idlib region as the last major area under rebel control.
The war monitor said Russia had carried out air strikes in Idlib early on Monday that killed "at least 13 Syrian and non-Syrian fighters" from Hayat Tahrir Al Sham, the dominant rebel group in the region.
Several other fighters were wounded in the strikes, with some in critical condition, according to the Britain-based monitor, which relies on a network of sources inside Syria.