"The doctors have decided to send him home as the diagnostic procedure he underwent did not indicate anything seriously wrong with him," Zuma said in a news release posted on his Web site.
Earlier, Minister of Defense Lindiwe Sisulu told BuaNews that reports Saturday Mandela, 93, was admitted to the hospital for undisclosed surgery were false.
"The reason we took him to hospital was he did have a discomfort, on an ongoing basis," she said. "In fact, I looked at some of the pictures that are in the newspapers today and I wished that you had had his most recent picture."
She said Mandela had undergone a diagnostic laparoscopy to look for the cause of abdominal discomfort that had been bothering him for some time.
Last year, Mandela was hospitalized with a severe respiratory infection.
His last public appearance was in 2010 when South Africa hosted the World Cup.