Mr Zuma also told a news conference the 95-year-old former South African president remained in a critical but stable condition and was responding to treatment.
Mr Mandela returned to his Johannesburg home on Sunday after spending 87 days in a Pretoria hospital for a recurring lung infection.
Mr Zuma said: "We feel really good he reached a point where the doctors who were treating him felt he could now leave the hospital, which now indicates the progress he had made. We acknowledge he is old and is not well but we are very happy he has gone home, that he is still with us."
Mr Mandela will be receiving the same level of care at his house, which has been kitted out with medical facilities.