The plane, from Emirati airline Flydubai, issued a type of alarm signal before disappearing from flight-tracking sites, The Times of Israel reports.
Initially, there were concerns that the plane had been hijacked, but this was later dismissed.
Around 180 Israeli passengers were on board. The plane has now landed in Saudi Arabia and the situation is said to be under control. Passengers will now be brought home to Israel, Prime Minister Benjamin Netanyahu's office announced, according to Haaretz.
The plane turned sharply as it entered Jordanian airspace. In doing so, it also appears to have dived sharply in the air - from an altitude of around 10,000 metres to 5,000 metres, according to flight-tracking sites.
A "violent clash" between the pilots is believed to be behind the incident. Among other things, an investigation is under way into whether a stabbing incident occurred, according to Israeli i24.
"We heard screams on the plane. Then they opened the cockpit and we saw blood, and someone had stabbed the pilot with a pocket knife," a passenger told Keshet 12 television channel.
Israeli Prime Minister Benjamin Netanyahu and Defence Minister Israel Katz convened for an emergency meeting, according to media reports. Israeli fighter jets are reported to have taken off at the first alarm.
