Mandela left hospital on Wednesday, after nearly three weeks of in-patient treatment for a recurrent lung infection and surgery to have gallstones removed.
The 94-year-old is now convalescing at his Johannesburg home, where he received visits from friends, family and a handful of well-wishers delivering flowers and other gifts.
"Madiba is doing great and he is enjoying his family," Mandela-Dlamini told AFP via text message.
Mandela-Dlamini is the eldest daughter of Nelson Mandela and Winnie Madikizela-Mandela.
She was due to begin an ambassadorship in Argentina this year, but her arrival was delayed by her father's illness.
The revered former statesman was flown to a Pretoria hospital on December 8 from his rural ancestral home in Qunu.
Since then family members have asked for their privacy to be respected. On Friday they called for an end to speculation that he has been sent home to die.
"That is absolutely not true. My grandfather is well," grand-daughter Zaziwe Manaway told CNN on Friday.
"It can be very, very hurtful for us to hear these messages out there in the social media that our grandfather is going to go home to die. It is insensitive."
"My grandfather still wakes up in the morning (and) reads the newspaper, so is also aware of what is being said around him."
The government has provided little information about his health, leading to speculation about the status of the global icon.
On Wednesday the presidency announced that Mandela had made "sufficient progress to be discharged."
"Right now the doctors have considered it necessary and good that he should be in Houghton so that he's close to all the facilities where they can give him high care," presidential spokesman and former Mandela prison mate Mac Maharaj said on Thursday.
Mandela became an international hero after spending 27 years behind bars for his belief in democracy.
He garnered further admiration through his willingness to extend the hand of peace to his white captors and is widely credited with stopping a bloodbath when minority rule was overthrown and the first multi-party elections were held in 1994.
Once a spry boxer who stayed fit during his long years behind bars by doing calisthenics in his cell, he has grown increasingly frail in recent years, and he exited public life in 2004.
In February, Mandela spent a night in hospital after receiving a minor exploratory procedure to investigate persistent abdominal pain.
In January 2011, Mandela set the nation on edge when he was hospitalised for two nights with an unnamed acute respiratory infection, which the government initially described as "routine" testing.
While serving his 27-year prison term, Mandela was diagnosed with early-stage tuberculosis in 1988, a disease that killed his father.