The Syrian state news agency SANA reported: "At dawn, the Zionist enemy carried out a new aggression against one of our military bases in the centre of the country.
"Our air defences repelled it and hit more than one plane."
The Israeli pilots of the crashed F16 were reported to be alive.
The exchange of fire was the most serious between arch emnemies Israel and Iran since the start of the civil war in Syria in 2011.
It marked the first time Israel publicly acknowledged attacking what it identified as Iranian targets in Syria since war broke out.
The Israeli military issued a warning to Tehran, saying it was responsible for the drone that entered Israel.
In recent weeks Israel has repeatedly warned against the presence of Iranian forces in neighbouring Syria.
Israel has carried out dozens of air strikes on the Syrian armed forces and their allies since the civil war started.