Despite the incident, the aircraft was able to land safely and the team are continuing their preparations for their group game against Uruguay on Wednesday.
A statement from the Saudi Football Federation said no-one was hurt after a "minor technical malfunction".More news: Rescued migrant ship arrives in Spain
Unverified video footage showed the wing of the aeroplane in fire.
"According to the Saudi Arabian Football Federation, all the Saudi national team players have arrived safely in Rostov-on-Don this afternoon to play against Uruguay, and now are staying in their residence, and that the fire was merely an accident", one of the statements said.
Saudi Arabia was drawn into Group A and lost its World Cup opener 5-0 to host nation Russian Federation. That puts them in a must-win situation against Uruguay, favourites in Group A. They'll face Egypt in their final group-stage match on Monday, June 25.More news: Magnitude 6.1 quake strikes Osaka
Saudi Arabia will face Luis Suarez and Uruguay in its next match.
But Group A favourites Uruguay are still widely expected to clobber Saudi Arabia, the second-lowest World Cup team in the Federation Internationale de Football Association rankings at No. 67.More news: Thousands cheer Meghan and the Queen on their day out in Cheshire