"Charlie Hebdo has again published cartoons insulting the Prophet and this is an extremely stupid act," a statement read on IS's Al-Bayan radio said, AFP reported.
The cover in question features a cartoon of the Prophet crying, holding a sign which reads "Je suis Charlie" (I am Charlie) under the caption "Tout est pardonne" (All is forgiven).
Most of the three million copies of the new issue of Charlie Hebdo going on sale this morning have already been sold out. This compares with a normal print run of 60,000 copies for the magazine. The satirical weekly has also been translated into six languages, including English, Arabic and Turkish, publishers have said. All profits from the issue will go to the victims' families.
On January 7, Charlie Hebdo's Paris office was attacked by gunmen, who murdered 12 people and injured another 11. Two of the terrorists responsible for the attack were later shot by police after an extensive manhunt, and a third suspect turned himself in.
Hours prior to the attack, the magazine had posted a caricature of the leader of the Islamic State militant group on its Twitter page. The satirical magazine has been known for decades for its unrestrained literary and artistic criticism of every conceivable topic, including religion. Its editors had received several death threats in years past for its publication of cartoons featuring the Prophet Muhammad; its offices were firebombed in 2011.