French embassies, consulates, cultural centers and international French schools in some 20 countries will be closed on Friday as a precaution.
Government ministers voiced concern at the Charlie Hebdo cartoons but defended the freedom of the press.
Riot police have been deployed around the magazine’s offices in Paris.
The magazine has confirmed that its website has been attacked. It was not accessible as of Wednesday morning.
Its paper edition features caricatures which play on both the uproar in the Islamic world over an amateur video which mocks Islam and the row over the publication in France of topless photos of the Duchess of Cambridge.
A tenet of Islam bans the portrayal of its founder, the Prophet Muhammad.
Some 30 people have died in violent protests which erupted early last week over the Innocence of Muslims video, which was made in the United States.
The dead include the US ambassador to Libya, Christopher Stevens, and three other Americans, who died in Benghazi. US and other Western embassies have come under attack in mainly Muslim countries.(BBC report)