Israeli media, citing security officials, said the incident on Wednesday stemmed from a feud between the plane's two pilots, and everyone on board was safe.
The plane landed in Tabuk, a civilian and military base in the kingdom.
The FlyDubai plane had transmitted an emergency alert, according to publicly available flight tracking information.
About two-and-a-half hours after departing from Dubai, it abruptly descended from 10,000 metre to 5200m within a minute before making an erratic circle close to the Jordanian border and eventually landing in Tabuk about an hour later, according to FlightRadar24.
A regional official briefed on the incident said a fight broke out in the cockpit and apparently involved pilots.
It was not immediately clear what had caused the fight, the official said.
"The crew have been questioned as part of the investigation," the regional official added but did not say if anyone had been detained.
An Israeli official said Israel believed the incident might have been an attempt to attack Israelis, but the investigation was ongoing.
A third official confirmed that Israel had scrambled warplanes, fearing a hijacking of a plane carrying dozens of its citizens.
Israeli Prime Minister Benjamin Netanyahu has warned in recent days of unspecified, escalated security threats.
Netanyahu's office said the situation was under control and Israel was working to bring the passengers home.
Emergency landings for personnel reasons are rare yet not unheard of.
Passengers told Israel's Ch 12 by phone that they heard shouts from those sitting more forward on the plane who heard the altercation between the pilots, and the plane dipped steeply before landing in Saudi Arabia.
They also said that all the passengers were staying on the plane and that there was a heavy presence of Saudi security forces surrounding them.
FlyDubai later confirmed that flight FZ 1073 on the way to Ben Gurion experienced an incident and landed safely in Tabuk on Wednesday.
"Our teams are working closely with the relevant authorities," the carrier said.
Flight-tracking data indicated that the plane was a Boeing 737 Max 8.
FlyDubai is the lower-cost sister carrier of Emirates airlines.
The UAE has become a popular holiday destination for Israeli tourists since the countries normalised ties in 2020.
Israelis were targeted in a string of hijackings and airplane attacks by Palestinian militants in the 1960s and 1970s.
Israel has not experienced a hijacking in decades but maintains some of the strictest airport security in the world, including often invasive check-in procedures for Israel-bound flights.
