A Syrian military official told state media the depot was hit, and three soldiers were injured. Syria said most of the missiles were intercepted.
Israel has not confirmed the strikes. It said it activated its air defence systems to bring down a Syrian missile.
There were no casualties or damage to property in Israel, the military said.
Late on Tuesday, Syria's state media published footage of an object moving over Damascus being intercepted.
A loud explosion is then heard, followed by burst of artillery shelling.
The Israel Defense Forces (IDF) have not commented on the reported air strikes.
The IDF later tweeted that its air defence systems were "activated in response to an anti-aircraft missile launched from Syria".