Erongo region crime investigations coordinator Erastus Iikuyu confirmed that the police were investigating a case of racial discrimination and defamation of character.
The 33-year-old man also claimed that he was told not to enter the bar again because "it is only for German people, not for blacks".
Iikuyu said an arrest was pending to enable the finalisation of the investigation.
"We take racial discrimination very seriously, hence our investigations," he said.
The owner of the restaurant, whose name and the name of the business will not be disclosed now, told The Namibian about the "troublemaker" whose behaviour forced him to call the Swakopmund Neighbourhood Watch to remove him.
He said the customer was talking loudly inside the restaurant, and disturbing everyone else.
"I asked him to stop and go outside, but he went crazy, and said we live in a free Namibia. There were lots of witnesses. We also have it on CCTV," the owner explained. "He also told me he would come and shoot me in front of my customers."
According to him, a white customer, who allegedly knew the black customer, pushed him outside.
"I did not hear anything about 'black baboon', or this being a German restaurant and black people not being allowed. This is nonsense. We have lots of black and white customers. I am even married to a woman of colour. Racism is not an issue with us," he stated.
Asked if a charge was laid against the customer, the owner said he often experiences disturbances as part of the restaurant business, especially when alcohol is involved, and it gets sorted out without criminal procedures.
"On the night, there will be problems may be, but the next day we greet each other again, and they come to enjoy at the restaurant again," he noted.
Police spokesperson Kauna Shikwambi said they would take the matter seriously if allegations have merit.
She said racism is a "very complex matter" between all colours, and many times it is rooted in the former apartheid era.
"We cannot and should not tolerate it anymore. We should move on. It does not serve a purpose anymore. If any Namibian makes themselves guilty of racial slurs, they will be charged for the crime," she said, adding that being intoxicated is no excuse to be racist or to use racial slurs.