The decision to give the 1990s teen drama the restrictive rating had attracted criticism online, but the board explained its decision in full on its official website.
"One episode in this TV series contains a scene in which a child character hides inside a tumble drier," the BBFC said.
"The presentation of this behaviour is comic and no negative consequences are shown which would warn young viewers of the potential dangers of hiding in such appliances.
"While fatal incidents of children trapped in washing machines or fridges are rare, there remains sufficient cause for serious concern."
It continued: "The distributor indicated that they would be happy to accept a higher certificate rather than cutting the episode.
"The TV series is rather dated and would not have much appeal to a young audience when compared to current children's TV programmes."
The BBFC added: "In addition, as the work was being targeted at an adult 'nostalgia' market, children would not be the 'natural' audience.
"The BBFC decided - given the work's history, the company's willingness to accept a higher certificate and that the work was not being aimed at children - to pass it '15' without cuts."
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Watch the introduction for The Secret World of Alex Mack below: