Some, like eNCA (DStv 403), the SABC and Sky News (DStv 402) refuse to.
The new Charlie Hebdo cover - arguably the most newsworthy image of 2015 - comes after the killing of 12 journalists in Paris, France last week working at the satirical publication, a story which dominated global news headlines.
While several TV outlets and newspapers are showing it, some are not.
The new Charlie Hebdo cover shows a cartoon of Muhammad against a green background, shedding a tear and saying "I am Charlie", together with a headline, "'Tout est pardonné" (All is forgiven).
Despite the huge news value of the cover image and the need to place the news and story in proper context for viewers, some news organisations fear some form of religious reprisal or causing offense if they show the image which is considered a sin to Muslims to depict.
That makes it difficult for viewers who might only rely on one specific type of news media, or watch one TV news channel, to get a true sense of what the offending cartoon looks like or to understand what all the fuzz is about, says Margaret Sullivan, The New York Times' public editor.
eNCA is responding to a media enquiry earlier this week asking what eNCA's decision is regarding the showing or censoring of the new Charlie Hebdo, and the reasoning behind the decision.
"Defending freedom of expression is a core value of ours. But freedom to express is also the freedom to determine what you don't depict," says Patrick Conroy, managing director of eNCA.
"We have different editorial criteria at eNCA to Charlie Hebdo. We have supported satire vigorously through LNN. We are undoubtedly the leaders in TV satire in South Africa".
"But we cannot be forced to concur with Charlie Hebdo's provocative style because of the terrible tragedies in France".
"Depicting the Prophet Mohammed is deemed offensive to many and unless a greater public interest is served for our audience we respect those sensitivities".
"You cannot have editorial policies that waver because others, like Fox News, have chosen to show the cover page. We're not scared - we are respectful. (On a point of consistency we did not show the Danish cartoons in 2005 either)".
"Those who want to actively seek out these cartoons will do so online. On TV the viewer is dependent on us when it comes to what they will see, hence our approach," says Patrick Conroy.
"We will risk offense when we deem our Constitution and freedoms to be under threat. An important consideration here is that the Charlie Hebdo attacks failed in their objective to silence free speech".
"What will disrespecting the sensitivities of peace loving people after this tragedy achieve? For this reason my colleagues and I concur with CNN, SABC and ANN7," says Patrick Conroy.