Zuma visited Mandela, also a former president, at the Pretoria hospital, the official news agency SAnews.gov.za said.
"We continue to appeal to the media and the public to respect the privacy of Madiba and his family," said the presidency, using a term with which he is popularly known.
According to the presidency, Mandela was admitted for medical tests.
"Mandela will receive medical attention from time to time, which is consistent with his age. Madiba is doing well and there is no cause for alarm," an official statement said.
"We wish Madiba all the best. The medical team is assured of our support as they look after and ensure the comfort of our beloved founding president of a free and democratic South Africa," said Zuma.
