"Israel carried out an aerial aggression at 4:20 a.m. [01:20 GMT] on Friday, launching rockets from the occupied Golan Heights that targeted facilities south of Damascus," the source was quoted as saying.
Most rockets were downed by the Syrian air defence, the source said.
"The aggression left one civilian injured, as well material damage," the source added.
Israel occupied the strategic region of Golan Heights in 1967. It has since used it to carry out occasional attacks on Syria targeting what it says are Iranian-supported militants. The latest attack in May killed three civilians.