The incident occurred on Wednesday, 30 September, aboard flight FZ1073, which was heading to Ben Gurion Airport.
Flight-tracking data indicated that the aircraft lost more than 17,000 feet, around 5,200 metres, in less than two minutes.
According to accounts from passengers and Israeli authorities, one of the pilots attacked his colleague inside the cockpit. During the incident, passengers and crew members managed to intervene and restrain the alleged attacker.
Two other Flydubai pilots who were travelling on board later took control of the aircraft and managed to make a safe landing at Tabuk Airport, in north-eastern Saudi Arabia.
Flydubai confirmed that the flight had experienced an incident during the journey and was diverted to Tabuk, adding that the passengers were safe.
The injured pilot received medical assistance after landing, while the alleged attacker was taken into custody by Saudi authorities.
Israeli authorities said initial indications pointed to a possible deliberate attempt to bring down the aircraft, but the motive behind the attack remains under investigation.
The airline has not confirmed that interpretation and said it is cooperating with the authorities investigating the circumstances of the incident.
Following the landing in Saudi Arabia, the passengers were later transported to Tel Aviv on a replacement flight.
The incident also prompted Israeli authorities to announce tighter security checks for pilots operating flights to the country.