The cartoon was drawn by Zapiro in response to a Facebook user who started a page called "Everybody Draw Muhammed Day!"
Courts in Pakistan recently blocked Facebook and Youtube for hosting "un-Islamic content".
Muslims consider any depiction of the prophet as blasphemous.
"It seems to be provocative in many ways on the very eve of the World Cup in South Africa," Ihsaan Hendricks, the president of South Africa's Muslim Judicial Council, said.
"We need peaceful co-existence and co-operation amongst religious communities in South Africa."
The Mail & Guardian said it received a flood of angry calls on Friday, following the publication of the cartoon.
The publication said the Council of Muslim Theologians had raised the spectre of a violent backlash during the World Cup, which kicks off on June 11, in arguments before the court requesting an injunction against the cartoon.
"My view is no cartoon is as insulting to Islam as the assumption Muslims will react with violence," Nic Dawes, editor of the Mail & Guardian, said.
South Park row
The row is the latest in a string of incidents involving images of the prophet.
The creators of the American TV cartoon South Park have faced death threats after an episode showed the prophet wearing a bear costume.
Zapiro, whose real name is Jonathan Shapiro, said he was not trying to offend Muslims.
"I believe that all religions should be subjected to satire and that some religious groups should not be able to think they are above society," he said.
"Some of the people who have been criticising me are the same ones who applaud cartoons about Israel on infringing Palestine's rights."