Police in South Africa have arrested the youngest son of Zimbabwe's late former President Robert Mugabe, who is facing a charge of attempted murder after a reported shooting at a property in an upmarket suburb of Johannesburg.

Bellarmine Mugabe, 28, was taken into custody after a 23-year-old man, believed to be a gardener, was shot and injured.

Officers searching the house in Hyde Park, where Mugabe was staying, have found bullet cartridges but no firearm, police have said. 

Bellarmine Mugabe is the youngest son of Robert and his second wife Grace Mugabe. Robert Mugabe, who died in 2019, led Zimbabwe for 37 years before being forced out of power at the age of 93 in 2017.

One other man has been arrested alongside Bellarmine Mugabe as investigators continue their work, police spokesperson Col Dimakatso Nevhuhulwi said.

The pair are expected to appear in court "soon", according to a police statement.

Police are not yet officially naming Bellarmine Mugabe as one of those arrested, but reporters at the scene saw him in handcuffs and he has been widely named by local media.

The victim is in hospital and in a critical condition after being shot once, the spokesperson added.

In a briefing outside the property, Nevhuhulwi said the two suspects have not "told us where the gun is, they are not saying anything about the gun".