As newspaper kiosks around Paris put up "sold out" signs, it was announced that an extra two million copies of the newspaper will be printed to meet demand.
Newspaper kiosk owners reported they had queues of people waiting to get their hands on a copy by the time they opened up.
A total of 700,000 issues of the magazine, which was the victim of a deadly Islamist killing a week ago, were distributed early Wednesday but other copies of the magazine will be made available for sale throughout the week.
Charlie Hebdo contributor Patrick Pelloux tweeted his thanks to everyone who bought a copy and said more would become available.
Rupture de Charlie hebdo partout! Alors d abord merci et rassurez vous on va réimprimer er re distribuer ! #CharlieHebdo— Patrick Pelloux (@PatrickPelloux) January 14, 2015
"There was a queue stretching around the corner from about 6am this morning. After a few minutes they were gone," one kiosk owner at the Juares in the 19th arrondissement told The Local as he turned disappointed customers away.
"We're hoping we'll get another delivery tomorrow," he said.
Another woman working at a newspaper kiosk in Paris told AFP: "It was incredible. I had a queue of 60-70 people waiting for me when I opened. I've never seen anything like it. All my 450 copies were sold out in 15 minutes."
The front cover shows a cartoon of the Prophet Mohammed holding a sign that says "Je suis Charlie" ("I am Charlie"), the slogan taken up by millions of supporters around the world after 12 people were gunned down in an attack on the magazine's Paris offices.
Around three million copies have been printed, which dwarfs the normal print run of around 60,000 copies, and the edition will also be available in English, Spanish, Italian, Arabic and Turkish.
The paper said on Wednesday however that the another two million copies will be distributed to meet demand, not just in France but around Europe.
Contrary to what was previously announced, no copies of the special edition of Charlie Hebdo were available in French-speaking Switzerland on Wednesday morning, Swiss broadcaster RTS reported
Within hours of the edition coming out there were reports of copies being sold on eBay for hundreds of euros.
"The editor decided this morning to increase the print run to five million," said Veronique Faujour, head of press distribution firm MLP.
Many people who were disappointed at not being able to get their hands on a copy told The Local they had never bought the magazine before but wanted to show their solidarity with those who were killed.
"The more we buy, the stronger we are and the stronger the message is that we send to the people who carried out these attacks," one student named Elise, told The Local.
Another woman named Carole said: "I wanted a copy for symbolic reasons and to show solidarity with the movement that we have seen in France in the last few days."
Another disappointed customer named Brigitte dismissed the idea that the magazine should not have depicted the Prophet Muhammad on the front cover.
"It's not a question of angering Muslims. We live in a secular country. If they don't like secularism, does that mean we all have to be secular?
"It's a just a question of tolerance, we tolerate the fact they can wear the veil and the djellaba and they should tolerate the fact we are secular.
"It's bizarre to think that the drawing is an insult, if they were really religious they wouldn't believe that a drawing can depict the prophet."
Although this week's edition of Charlie Hebdo features just one cartoon of Muhammed, the paper does include several drawings mocking jihadists.
Money from sales will go to the victims' families.
Muslim leaders in France, many of whom believe any depiction of Muhammad is sacrilegious, had called for calm ahead of the release of the paper.
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