Michael Acton Smith, who has run the business for 10 years, said he wanted to focus on a "more creative role" rather than the day-to-day running of the firm.
Divinia Knowles, currently chief operating and financial officer, will become president.
A new chief executive will be announced at a later date, the company said.
Moshi Monsters is one of the world's most popular children's social networks, with around 80 million users.
The service operates through paid subscriptions. But it is associated merchandise - plush toys, music albums and other spin-offs - that generate around half of Mind Candy's revenue.Divinia Knowles, who has been at the company for eight years, has been made its president
But analysts say the company had been slow to adapt to the mobile games market, in particular the "freemium" business model - the approach that gives away products for nothing, but encourages small payments within an app or other type of game.Growing globally
The company has launched mobile products, including some freemium services, but now needs to build their reputation.
Ms Knowles told the BBC that her role was to raise the profile of other products such as World of Warriors, aimed at older children, and PopJam, a "creative community for kids".
"Moshi has been absolutely amazing. But Mind Candy has gone from being a one-product company to multiple products. The business now is much more complex than it used to be.
"Michael is known as 'Mr Moshi'. It's now about taking us more to being Mind Candy."
A major part of this process will be increasing international reach.
"Moshi was great in the UK but never really smashed it out of the park in the US," Ms Knowles added.
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