The decision follows the announcement that the channel will stop broadcasting Big Brother after its final run next summer, The Guardian reports.
Head of Channel 4 Julian Bellamy said: "The decommission of Big Brother earlier this year has been the catalyst for a process of creative renewal right across Channel 4.
"When Wife Swap launched, it was a truly groundbreaking programme which heralded an era of new factual formats right across television.
"It was challenging, impactful and connected with a large mainstream audience. I am now looking to find new ways to challenge the mainstream through entertaining and provocative programmes."
Bellamy added that both Wife Swap and How Clean Is Your House? had been "huge hits" and were still profitable, but the cancellation was a "creative decision on our part to make space for new ideas".
No new episodes of either show will be made for the channel.