The response was the “most significant attack” of its kind against Syria since the 1982 Lebanon war, said senior Israeli air force general Tomer Bar.
The F-16 jet went down during a mission that followed an Iranian drone launch into Israeli territory, Israel says.
The two pilots parachuted to safety before the crash in northern Israel.
Israel says it responded with a second wave of strikes on both Syrian and Iranian military targets operating inside Syria.
Israeli air strikes in Syria are not unusual, BBC Middle East correspondent Tom Bateman says, but the loss of an Israeli fighter jet marks a serious escalation.
Later on Saturday, Israeli Prime Minister Benjamin Netanyahu held a meeting with his military chiefs. He said Israel wanted peace but would defend itself “against any attack against us or any attempt by Iran to establish itself against us in Syria”.
Israel’s military says one of its combat helicopters downed an Iranian drone infiltrating Israel. It tweeted footage of the incident.
Israeli aircraft then attacked Syrian and “Iranian targets in Syria”, the military says.
Syria’s state media say air defences opened fire in response to an Israeli attack on a military base, hitting more than one plane.
The damaged F-16 came down in an empty field near the town of Harduf in northern Israel. (Courtesy BBC)