The latest edition uses a map of the country, renamed "Skintland", with puns instead of place names such as "Glasgone", "Edinborrow" and the "Highinterestlands".
It is followed by an article concluding that independence would come at a high price and could leave Scotland as "one of Europe's vulnerable, marginal economies".
Mr Salmond wants to hold a referendum on independence in autumn 2014.
The Scottish National Party leader said the front cover displays a sort of "Bullingdon Club humour" of "sneering condescensions".
"It just insults every single community in Scotland," he told Radio Clyde.
"This is how they really regard Scotland. This is Unionism boiled down to its essence and stuck on a front page for every community in Scotland to see their sneering condescensions.
"They shall rue the day they thought they'd have a joke at Scotland's expense."
Mr Salmond added: "This doesn't represent England. Goodness' sake, I wouldn't insult the people of England the way the Economist believes it should insult the communities of Scotland.
"This is a particular strata of London society. It's not a very attractive strata. They're not even funny, let's face it. If it was a decent joke we'd have a laugh at it. This is just plain insults."
Nicola Sturgeon, the Deputy First Minister, tweeted: "I'm pretty sure that Scots who don't support independence will find this week's @TheEconomist cover every bit as offensive as those who do."
The magazine article states: "If Scots really want independence for political and cultural reasons, they should go for it. But if they vote for independence they should do so in the knowledge that their country could end up as one of Europe's vulnerable, marginal economies.
"In the 18th century, Edinburgh's fine architecture and its Enlightenment role earned it the nickname 'Athens of the North'. It would be a shame if that name became apt again for less positive reasons."