Robert Mugabe Jr, 33, was arrested on Wednesday morning as he drove the wrong way down a one-way street, according to court documents. Police searched a black sling bag he was wearing at the time and allegedly found two small sachets of cannabis.
Following the incident, police said in a statement that five people in a "syndicate linked to him" were also arrested.
Mr Mugabe's lawyer told the BBC they plan to deny the charges, and contested the factual claims made by the police.