Their split comes just seven months after their wedding, which followed a whirlwind romance that begun on Twitter.
A source told The Sun that the 15 year age-gap became "too much", and that the split wasn't entirely down to Mel's arrest.
"It's not a case of Mel ending the marriage because Jack called the police. But what happened was obviously an indication that things weren't right," they said.
"It's hard to see how they're going to be able to make the marriage work. The pressure has been just too intense."
It is believed the pair haven't seen each other since Mel was taken by police from their north London home.
She spent a night in the cells and was later released with a caution for common assault.
Earlier this week, Jack deleted his Twitter account, after posting a tweet about a black eye.
He posted a picture-message which read "If I have 10 pieces of bacon and you take 5 what do you have? That's right, a black eye and a broken hand."
He wrote alongside it: 'Saw this and thought of my wife! @ MsMelanieSykes # MmmmmBacon'
Just 12 months earlier the pair had been swapping racy tweets to each other, as Mel bragged that she had "the giddiest knickers of my life" and the "the raging horn".
On Sunday, Mel announced her return to the site, after a silence following her arrest.
She tweeted: "A huge thank you to all my supporters. I love you guys. Xxxxxxxxxxxxx."
Orlando Bloom and Miranda Kerr
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Joey Essex and Sam Faiers
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Harry Styles and Taylor Swift
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Spencer Matthews and Louise Thompson
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Spencer Matthews and Lucy Watson
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Cheryl Cole and Tre Holloway
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Chris Brown and Karrueche Tran
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Clint Eastwood and Dina Eastwood
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Miley Cyrus and Liam Hemsworth
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Nicole Scherzinger and Lewis Hamilton
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Denise Van Outen and Lee Mead
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Kelly Brook and Danny Cipriani
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Andy Jordan and Louise Thompson
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Kylie Minogue and Andres Velencoso
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Kris and Bruce Jenner
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Liam Gallagher and Nicole Appleton
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Britney Spears and Jason Trawick
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Marc Jacobs and Harry Louis
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James Arthur and Rita Ora
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Simon Cowell and Carmen Electra
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Richard Gere and Carey Lowell
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Lily Collins and Jamie Campbell Bower
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Robert Pattinson and Kristen Stewart
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