Mandela, born in 1918, is alert and playing with his grandchildren, Manaway said.
"That is absolutely not true. My grandfather is well. 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," she told CNN.
She said she wants to appeal to people spreading those rumours to stop, and to be more sensitive to the family and to Mandela, a global icon of peace.
"My grandfather still wakes up in the morning, reads the newspaper. So is also aware of what is being said around him," Manaway said.
Mandela was treated for an acute respiratory infection in 2011. He was hospitalised for a lung infection Dec 8, and underwent surgery Dec 15 for removal of gallstones.
Because Mandela is in his 90s, it was understandable that "once in a while, he needs medical care and medical attention. And we're very grateful he's surrounded by the best medical team. He's very well taken care of, and he's very comfortable, and he's very happy", she said.
A spokesman for South African President Jacob Zuma said earlier that Mandela would continue receiving treatment at his home in Houghton.
Washington: South Africa's first black president Nelson Mandela, at home after a long hospital stay, is aware of social media rumours that he is close to death, his granddaughter Zaziwe Manaway told CNN Friday.
First Published: Friday, December 28, 2012, 23:12