The incident happened last week and emerged after a video went viral online showing a friend of 25-year-old Thabiso Danca - Christopher Logan, who is white - confronting what appears to be the pub's manager.
In it, Logan says Danca tried to enter the pub shortly after his friends during a night out in the touristic city, but was blocked by a bouncer who told him black patrons were admitted only if accompanied by a white person.
"You don't have the right to discriminate in this country, it's a crime," Logan is heard saying.
The government urged police to probe "with speed" the "appalling" and "racist incident", which it said saw Danca denied entry at Hank's Olde Irish pub in Cape Town.
"It is horrifying and outrageous that the tendencies of apartheid South Africa keeps rearing its ugly head," cabinet spokeswoman Phumla Williams said in a statement.
A man who declined to give his name, answering the Hank's Olde Irish pub telephone on Tuesday, said he had "no comment" as he waited to speak to his lawyer.
The pub was closed on Tuesday. A note on the door described the accusations as "unfounded and unproven", adding the owners and staff have received threats and were physically assaulted by the "primary individual" in the viral video.
"We as the owners have never - nor have we ever instructed our staff - to discriminate on any basis whatsoever," the note read.
The radical leftist Economic Freedom Fighters party called for a picket outside the eatery on Tuesday, saying the incident was not an "isolated" one but "structural and endemic".
Last month, a woman was arrested after a WhatsApp voice message circulated on social media seeming to call for black people to be banned.
South Africa remains deeply divided along racial lines almost three decades after Nelson Mandela came to power vowing national reconciliation following the end of white-minority apartheid rule.