They suffered a scare on Monday as there was reportedly a brief fire in one of the engines on the plane carrying the team.
The players could be seen leaving the plane - a Russian Airlines Airbus A319-100 - shortly after landing.
Thankfully, the plane landed safely at Rostov-on-Don Airport and no one was harmed.
The statement was followed up by a tweet from the federation's official Twitter account.
A video of the horrifying incident surfaced online.
Bizarrely, two-time World Cup champion Uruguay has never beaten the Green Falcons; Saudi Arabia won a friendly in 2002 while a 2014 friendly ended in a draw.
Uruguay squad: goalkeepers: Fernando Muslera, Martin Silva, Martin Campana; defenders: Diego Godin, Sebastian Coates, Jose Maria Gimenez, Maximiliano Pereira, Gaston Silva, Martin Caceres, Guillermo Varela; midfielders: Nahitan Nandez, Lucas Torreira, Matias Vecino, Rodrigo Bentancur, Carlos Sanchez, Giorgian De Arrascaeta, Cristian Rodriguez, Gaston Ramirez; forwards: Cristhian Stuani, Maximiliano Gomez, Edinson Cavani, Luis Suarez.
Blaming nerves for their underwhelming 1-0 opening World Cup win against Egypt, Uruguay vowed to be sharper and faster when they face Saudi Arabia on Wednesday.
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