The storm has damaged Celta's Balaidos stadium, affecting the area reserved for away fans, leading to inspections from the city's local council on Saturday morning and the mayor of Vigo saying "the game needs to be postponed".
La Liga confirmed the postponement on Saturday night and said that the exact date for the fixture to be played is yet to be decided.
"Following a report from the city of Vigo, the organisation believes that Balaidos Stadium is not safe for spectators and players to attend on Sunday, February 5," a statement released on its website said.
"Therefore, having received this information, La Liga and the Real Club Celta have transferred this report to the Spanish FA (RFEF).
"La Liga will propose possible dates to the clubs and broadcasters, and the president of the RFEF will decide on the matter."
The scrapping of the Celta-Real Madrid fixture will deprive Cristiano Ronaldo of the chance to score on his 32nd birthday.