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Zumas supporters protest his imprisonment in Johannesburg on Sunday
Photo: KIM LUDBROOK / EPA
The riots in South Africa have already led to an estimated damage of 100 million rand (the equivalent of six million euros) within days, said a government spokesman.
They started on Thursday in the home province of Zumas in the east of the country, KwaZulu-Natal.
A group of around 800 demonstrators shot and injured police officers in Gauteng Province, the police said in a statement.
A 40-year-old man was shot dead;
who was responsible for the death is still being determined, it said.
Protesters also blocked numerous streets and looted shops.
Thousands of demonstrators had previously set dozens of cars, trucks and infrastructure on fire in KwaZulu-Natal and barricaded parts of the N3 motorway, the country's most important north-south link.
According to police reports, at least 62 demonstrators were arrested across the country.
Zuma was sentenced to a 15-month prison sentence last week for disregarding the judiciary, starting on Thursday.
The 79-year-old is in Estcourt Prison in KwaZulu-Natal.
It is the first time that a former president of the country has been jailed.
Zuma has to answer to a commission of inquiry for various allegations of corruption during his term of office (2009-2018), but did not accept a subpoena.
He had questioned the legitimacy of the commission several times and stressed that he would go to prison rather than appear.
On Monday, the Constitutional Court will examine Zuma's application for the annulment of the prison sentence - a procedure that is actually not provided for in a supreme court decision.
dpa / tfb