Late on Monday evening, the team had arrived at their hotel in the center of the city ahead of their second Group A match against Uruguay on Wednesday
A spokesman for airline Rossiya denied a fire had occurred and said a fault that developed was due to a bird strike.
The team was traveling on a Rossiya Airbus A319 from St Petersburg to Rostov-on-Don.
As it came into land, the plane “suffered a technical fault with one of its engines, with a bird getting caught seen as the preliminary cause,” a Rossiya airlines spokesman said.
Reports that of a fire in one of the engines were incorrect, the spokesman added.
Videos shared on social media showed an aircraft that posters identified as the Saudi team’s plane with its wing on fire while it was in the air.
The footage, which Reuters was unable to verify independently, was shared by civil aviation monitoring website Airlive.net, which said the fire broke out on the approach to Rostov airport.
The Saudi federation released photographs of the players smiling and looking calm as they boarded a bus for the Mercure Hotel in central Rostov.
The team, who are making their first appearance at the World Cup since 2006, suffered the biggest defeat in the tournament so far when they were thrashed 5-0 by hosts Russia in the opening game in Moscow on Thursday.