They said the fire was "merely an accident" and were quick to clarify that the plane was not owned by the team and was provided to them by the International Air Transport Association.
In their final game of the group, they take on Egypt, who play Russian Federation on Tuesday.
Incredible footage captured by the Saudi team showed flames engulfing the wing as the plane touched down.
U.S. to withdraw from UN human rights body
The United States has opted to stay out of the Human Rights Council before: the administration of President George W. The council is scheduled to discuss Israel and the Palestinian territories on July 2, according to its agenda.
The Saudi Football Federation posted videos the playing filmed re-assuring the public that they landed safely and no one was hurt in the incident.
They are expected to struggle again on Wednesday, with Uruguay eyeing up a second win after securing a late 1-0 victory over Morocco in their first game.
"The plane landed a few minutes ago at Rostov on Don Airport, and UNOMIG personnel are now safely heading to their residence".