President Jacob Zuma said Nelson Mandela is "responding very well to the treatment" as he urged the country not to panic.
He told BBC News: "Of course I have been saying to people, you should bear in mind Madiba is no longer that young and if he goes for check-ups every now and again, I don't think people must be alarmed about it. I would like to really say the country must not panic."
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His mother Princess Diana was killed in a car crash in Paris in 1997 when he was just 12 and his brother William was 15.
The 21-year-old, who was arrested on Sunday, also allegedly injured two other people in the attack in the German city of Reutlingen.
She was going to the aid of a family member who got out of the car in the middle of the park and was dragged away by a different tiger.