"We view this in a serious light given the resilience of racism in the South African discourse and the condescending attitude demonstrated by some elements in the media and society," spokesperson Zizi Kodwa said in a statement.
"Such attitudes particularly from the media reinforce the view that some sections of the media misuse the freedom of expression to undermine gains made thus far."
The party called the cartoon appalling.
The cartoon, titled "Congress of Clowns. And the clowns who voted them in", was posted on EWN's website, and depicted newly appointed ministers as clowns with big red noses.
On the side was another group of clowns, which were the voters, all in dark shading standing and watching with a description reading "we the poephols".
Kodwa said the ANC believed the media needed to counterbalance its freedom with responsibility and regard for the public.
"We expect the media to uphold democratic values and to reinforce responsibility based on ethical conduct," he said.
EWN on Thursday sent out a note saying it had read and heard its listeners' views and passed them on to the cartoonist.
"We at EWN apologise for any unintended offence caused. We at EWN will continue to strive for free speech and editorial independence," it said.