"Four Israeli planes penetrated our air space at 2:40 am (0040 GMT) via Lebanese territory and hit a military target on the way to Palmyra," the army said in a statement carried by state news agency SANA.
"Our air defence engaged them and shot down one warplane over occupied territory, hit another one and forced the rest to flee," it added.
The incident is the most serious between the two countries, which remain technically at war, since civil war broke out in Syria in 2011.
But it said none of those missiles had hit their targets.
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"This flagrant attack is part of the Zionist enemy's persistent efforts to support the terrorist gangs of Daesh," the Syrian army said, using an Arabic acronym for the Islamic State jihadist group.
"It will be responded to directly with all possible means," it added.
The Syrian army recaptured Palmyra from IS on March 2, three months after losing it to the jihadists for a second time. Syrian troops backed by Russian forces had first retaken it in March last year.