Axon, who is departing voluntarily, will leave at the end of April, but has no job to go to.
He said: "I am looking at various opportunities in the media industry and have had a great time at River, but am looking to take on a new challenge."
River chief executive Nicola Murphy will lead the hunt for a replacement for Axon, who has held several roles at River Publishing, including publisher, publishing director and managing director for the past two years.
Axon joined River Publishing from rival publisher John Brown, where he worked as group publisher on titles such as Viz and Bizarre. His departure follows River winning the brief to publish a new weekly title for WeightWatchers UK members, called Your Week.
Three hundred thousand copies of the magazine will be distributed to WeightWatchers members every week.
River Publishing's other clients include Harrods and Superdrug.
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