Matthew Weissinger, Director of Marketing at Epic Games, said that parents could claim a refund through the company's player support system.
Mr Weissinger was speaking at a meeting of the UK Government's Digital, Culture Media and Sport Committee on the subject of immersive and addictive technologies.
The Mirror reported that he said, "We have family fraud rules in place for just these exact types of situations.
"If they can show us that their child has done this transaction and it wasn't authorised, it's our intention to be generous in those cases."
Boy spent £1,600 on uncle’s card
The announcement comes after a six year old boy managed to spend £1,600 on his uncle’s card while borrowing his PlayStation account to play the game.
Asad Murad, 27, had reportedly been saving for a house when his nephew Alex spent the huge sum on in-game extras while he was playing Fortnite. The purchases were charged to Murad’s account, and he received the bill.
When asked how parents could prove that it was their children who had racked up the bill so that they could claim the money back, Mr Weissinger said the company would deal with it on a case by case basis.
This can include a number of transactions taking place in a short amount of time, as well as the name on the account being different to that on the card used to make the purchases.
Epic Games highlighted that there are a number of parental control features in the game that can be used to limit the way children can play Fortnite.