The Israeli army denied any planes had been struck
Israel said all its aircraft returned unscathed, although the Syrian army high command said the jet was struck by an anti-aircraft missile after it had flown back into Israeli-controlled territory.
It said it was one of four planes which "penetrated our air space at 2.40am (12.30 GMT) via Lebanese territory".
It added that an air defence unit hit another jet and "forced the rest to flee".
The Israeli military said its aircraft struck several targets in Syria and were back in Israeli-controlled airspace when several anti-aircraft missiles were launched from Syria toward the Israeli jets.
An Israeli military spokesman denied a jet had been shot down, adding: "At no point was the safety of Israeli civilians or the IAF (Israeli Air Force) aircraft compromised."
After a number of anti-aircraft missiles were fired from Syria, rocket sirens sounded in Israeli settlements in the Jordan Valley.
One of the projectiles was intercepted north of Jerusalem by Israel's Arrow air defence system.
A civil defence source told Reuters news agency the remains of the missile landed in a village on the outskirts of Irbid, northern Jordan, about 12 miles from the Syrian and Israeli borders.
The Israeli military did not confirm what was targeted, while Damascus described the operation as "blatant aggression" and an attempt by Israel to support "terrorist gangs" of Islamic State.
In recent years, both Israeli and foreign media have reported a number of Israeli airstrikes inside Syria targeting arms convoys of Lebanese militant group Hezbollah.
In January 2015, Jerusalem was blamed for an airstrike which killed six Hezbollah fighters and Iranian general Mohammad Ali Allah-Dadi in a Syrian-controlled area of the Golan Heights.