The controversial MailOnline columnist had sought to challenge the High Court’s initial ruling.
But Mr Justice Warby said that he had no jurisdiction at such a late stage to deal with the application for permission to appeal over the damages awarded. He added that none of the four grounds for appeal had "a real prospect of success".
Hopkins was ordered to pay Monroe £24,000 in damages and £107,000 to cover court costs earlier this month.
Mr Justice Warby ruled that she had libelled the food blogger in a tweet which wrongly accused her of vandalising war memorials.
She wrote: “Scrawled on any memorials recently? Vandalised the memory of those who fought for your freedom. Grandma got any more medals?”
She had actually meant to direct the abuse to New Statesman columnist Laurie Penny, who had said she didn’t “have a problem” with seeing graffiti on a memorial to women of the Second World War, which read: “F*** Tory scum”.
Shortly afterwards, Monroe offered Hopkins the chance to apologise and make a £5,000 donation to a migrant charity, or face legal action.
Hopkins refused and lost the libel case when it came to the High Court.
In his original judicial judgement, Mr Justice Warby noted: “The case could easily have been resolved at an early stage. There was an open offer to settle for £5,000. It was a reasonable offer.”
Instead, he said: “Ms Monroe is entitled to fair and reasonable compensation, which I assess at £24,000.”
Having her appeal rejected means she will now have to pay the £131,000 in damages and court costs.
The columnist's own legal fees are also expected to exceed £300,000.
After the second ruling in her favour, Monroe took to Twitter to clarify that the majority of the payment was to cover her lawyers' fees and would not go to her directly.
Hopkins has until Friday 7 April to pay the costs ordered by Mr Justice Warby.
She can still pursue her application to appeal directly with the Court of Appeal.
Monroe’s lawyer, Mark Lewis said in a statement that his client had "been vindicated in full from the libellous and wholly false accusation by Katie Hopkins that she had supported the vandalisation of a war memorial. Jack Monroe never did, and coming from a proud military family, never would."
He added: “Despite pointing this out to Katie Hopkins within minutes of her first tweet wrongly accusing Jack, Hopkins did not apologise. Rather the self-styled “rent-a-gob” defiantly posted another defamatory tweet.
“The price of not saying sorry has been very high. Hopkins has had to pay out of her own pocket a six-figure sum in damages and costs for a tweet that should have been deleted within minutes as soon as she was told it was wrong. On this occasion, the cost of renting that gob was particularly high.”