Chief Inspector Paul Carroll, of the National Fraud Intelligence Bureau, said: "Clearly you expect there to be more purchases of Fortnite over the Christmas period, it's the in thing for gamers. So it is certainly a time for parents to be vigilant and get their knowledge up to speed of what it entails.
"You have always got to question requests for personal financial information."
Many of the frauds came from children being tricked by scams on social media promisings free ways to get Fortnite's in-game currency, called V-Bucks.
V-Bucks can be bought with real money or earned playing the game and allow players to buy new items for their online Fortnite characters such as costumes, weapons or dance moves.
Since its release, Fortnite has become a huge hit with its free Battle Royale game, in which up to 100 people compete online in a last-man-standing shootout, especially popular.
The game's maker, Epic Games, recently revealed Fortnite now has more than 200 million players worldwide. The studio has previously warned players that online offers of free V-Bucks are not legitimate and not to participate in them.
Facebook and YouTube have since removed all the scam pages and videos found by the Sunday Telegraph.
A spokesman for YouTube said: "We use teams of highly trained content reviewers to determine whether videos violate our Community Guidelines and are committed to removing this offending content quickly."
Facebook declined to comment.