Three million copies of the weekly, featuring on the front page slogan "Je suis Charlie" ("I am Charlie") under the headline "All is forgiven", have been printed.
The magazine was sold out in many parts of the capital minutes after going on sale.
"Je suis Charlie" is the slogan taken up by millions of supporters in France and around the world after eight of the magazine's journalists and cartoonists and four other people were shot dead last week.
There are no other depictions of the prophet in the new edition, but many of the cartoons lampoon Islamist gunmen.
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The print run dwarfs Charlie Hebdo's normal run of around 60,000 copies, and the edition will also be available in English, Spanish, Italian, Arabic and Turkish.
"It was incredible. I had a queue of 60-70 people waiting for me when I opened at 5.45 am. I've never seen anything like it. All my 450 copies were sold out in 15 minutes," said a woman working at a kiosk in Gambetta metro station in Paris.
Cartoonist Renald "Luz" Luzier said he cried after drawing the front cover.
Some Muslims feel any depiction of the prophet is sacrilege, and Egypt's state-backed Islamic authority Dar al-Ifta denounced "an unjustified provocation against the feelings of 1.5 billion Muslims.