Two surface-to-air missiles were fired at the Sukhoi fighter jet, the Israel Defense Forces (IDF) tweeted.
According to Israeli reports, it happened over the Israeli-occupied Golan Heights. The pilot's fate is not clear.
Syrian news agency Sana said Israel had targeted the jet over Syrian airspace, but did not say whether it was hit.
Sana quoted an unnamed military source as saying the plane was conducting raids against "armed terrorist groups" near the southern Yarmouk Valley.
Syria routinely describes rebel groups as terrorists.
Israeli Prime Minister Benjamin Netanyahu later said that Syria had committed a "blatant violation" of a 1974 ceasefire agreement, which defines the lines of separation between the two sides' forces on the Golan Heights.
"We will not accept any intrusion... into our territory, either from the ground or from the air," Mr Netanyahu said, adding: "Our forces acted appropriately."
Israel's Haaretz news website said residents in northern Israel saw interceptor missiles fired and heard explosions.
Flames and smoke were also later seen rising from the area of the fence between Syria and the Israeli-occupied Syrian Golan Heights, AFP news agency reports.
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