Three million copies are being printed - a week after Islamist gunmen murdered eight journalists at the magazine and four other people in Paris.
The cartoon shows the Prophet weeping while holding a sign saying "Je suis Charlie" ("I am Charlie").
It is believed earlier cartoons of the Prophet prompted the attack.
The slogan "Je suis Charlie" has been widely used following the shootings.
In a separate attack in Paris two days later, four Jewish men died after an Islamist gunmen took hostages at a kosher shop in the French capital. A police woman was shot dead in a third shooting believed to have been carried out by the same attacker.
On Sunday, about 1.5 million people rallied in Paris in a show of solidarity with the victims
Security has been increased dramatically across France after the attacks
All copies of the magazine were sold out by Wednesday morning at this Paris newsstand
Referring to last week`s shocking events, French Prime Minister Manuel Valls said his country was at war with extremism and terrorism - but not with Muslims.
He was speaking on Tuesday after funeral ceremonies were held for seven of the victims in France and Israel.
France has deployed 10,000 troops at various sites across the country - including synagogues, mosques and airports - in response to the attacks.
Wednesday`s edition of Charlie Hebdo has an unprecedented print run of three million copies. Normally only 60,000 are printed each week.
Demand for what is being called the "survivor`s issue" of the magazine is high, correspondents say, especially as the proceeds will go to the victims` families.
People could be seen queuing outside newsstands on Wednesday morning to buy copies.
Kiosk owners told French media they had received large numbers of reservation requests, while at one shop in Paris all copies were reportedly sold out within 30 minutes.
