The president's decision comes after pressure from civil society organisations, Wise 4 Africa and the Soul City Institute.
The organisations cited assault charges laid against Mkhari by his wife.
They say while the charges were eventually withdrawn, Mkhari never accounted for his actions.
In 2018, Mkhari and his wife Ipeleng, were both arrested after opening charges of assault against one another.
"What we struggled with was what was expected of me and my family and Power [FM]," he said.
Mkhari said the organisations who raised these issues had never addressed or written to him.