The French government, which had urged the magazine not to print the images, said it was temporarily shutting down premises including embassies and schools in 20 countries on Friday, when protests sometimes break out after Muslim prayers.
Riot police were deployed to protect the Paris offices of satirical weekly Charlie Hebdo after it appeared with a cover showing an Orthodox Jew pushing the turbaned figure of Mohammad in a wheelchair. On the inside pages, several caricatures of the Prophet showed him naked.
The magazine's Paris offices were firebombed last November after it published a mocking caricature of Mohammad.
Essam Erian, acting head of the Egyptian Muslim Brotherhood's Freedom and Justice Party, said: "We reject and condemn the French cartoons that dishonour the Prophet and we condemn any action that defames the sacred according to people's beliefs."
Calling for a UN treaty against insulting religion, he added: "We condemn violence and say peaceful protests are a right for all. I hope there will be Western reaction condemning this."
A short film mocking Mohammad, posted on YouTube last week, sparked protests and outbreaks of violence in many countries.
The US ambassador to Libya and three other Americans were killed in an attack in Benghazi, and Western embassies were stormed in cities in Asia, Africa and the Middle East. Afghan militants said a suicide bombing that killed 12 people, including an Edinburgh woman, on Tuesday was in retaliation for the film.
One of the Charlie Hebdo cartoons – referring to the scandal over a French magazine's decision to publish topless photos of the Duchess of Cambridge – showed a topless, bearded character with the caption: "Riots in Arab countries after photos of Mrs Mohammad are published."
Charlie Hebdo editor Stephane Charbonnier said: "We have the impression it's officially allowed for us to attack the Catholic far-right but we cannot poke fun at fundamental Islamists.
"Everyone is driven by fear and this handful of extremists want to make everyone afraid."
French Foreign Minister Laurent Fabius criticised the magazine's move as a provocation. He said: "We saw what happened in Libya and in other countries. We have to call on all to behave responsibly."
The French Muslim Council accused Charlie Hebdo of firing up anti-Muslim sentiment at a sensitive time.
"The council is profoundly worried by this irresponsible act, which in such a fraught climate risks further exacerbating tensions and sparking damaging reactions," it said.
Richard Prasquier, head of the body representing France's Jewish community – Europe's largest – said religious censorship was wrong but added: "Publishing Mohammad cartoons at this time, in the name of freedom, is irresponsible."