A cartoon by award-winning satirist Jonathan Shapiro in the M&G on Friday shows the prophet grumbling to a psychiatrist about the furore in the Muslim world created by a Facebook page called Everybody draw Muhammad Day.
"Other prophets have followers with a sense of humour!" the turbaned, bearded figure, who is stretched out on the psychiatrist's couch, complains.
On Thursday evening, the M&G won an eleventh-hour court bid by the Council of Muslim Theologians to bar the publication of the cartoon.
The council had warned of a possible violent backlash and said the timing was bad, given the alleged threat to the cup.
"My view is no cartoon is as insulting to Islam as the assumption Muslims will react with violence," the newspaper's editor Nic Dawes said in defence of the drawing.
On Friday the paper reported it was receiving a flood of angry calls, and had even received death threats against the cartoonist.
A spokesperson for the Media Review Network, a group that lobbies on Muslim affairs, told Radio 702 he was "greatly" disappointed by the ruling and appealed for calm in the Muslim community.
Shapiro does his cartoons under the pen-name Zapiro.
His latest sketch comes days after an alleged al-Qaeda operative was arrested in Iraq on charges of terrorism, including a plot to target the World Cup.
Abdullah Azam Saleh al-Qahtani, a Saudi national, told journalists he had discussed with friends an idea to attack the Danish and Dutch teams or their supporters to avenge perceived insults in those countries against Muslims.
A Danish newspaper in 2006 sparked outrage among Muslims after publishing 12 cartoons of the prophet.
The Netherlands has seen a rise in anti-Islam sentiment in recent years since a Muslim murdered a filmmaker, Theo van Gogh, who had made a critical film about Islamic culture.