The raids early on Wednesday targeted military forces in Jamraya, 10km northwest of Damascus, the Syrian military said in a statement carried by state news agency SANA.
"This morning Israeli warplanes fired several missiles from Lebanese airspace on one of our military positions in the Damascus countryside," it said. "Our air defence systems blocked them and destroyed most of them."
UK-based monitoring group, the Syrian Observatory for Human Rights (SOHR), said some Israeli missiles did hit Syrian targets.
"Syria's air defence system blocked some of the missiles, but others hit ammunition depots near Jamraya," said SOHR chief Rami Abdel Rahman.
The Israeli military had no immediate comment on the accusations.
Syria's foreign ministry accused Israel of supporting armed groups that have shelled Damascus for days with "rockets and mortar rounds".
"The government of the Syrian Arab Republic reiterates its warning to Israel on the serious repercussions of its attacks on Syria, its continued support for armed terrorist organisations, and its continued occupation of the Arab territories," the ministry said.