Mandla Mandela, who is embroiled in bitter spat with family members over his grandfather's burial site, visited the former statesman at a Pretoria health facility on Sunday after missing his 95th birthday last week.
"The visit left me with a warm feeling because my grandfather is getting stronger and stronger everyday," he said.
In a statement, Mandla also issued a thinly veiled rebuke to his relatives after lawyers for more than a dozen family members had claimed in a court filing that the Nobel Peace Prize winner was in a "vegetative state".
Mandla said his grandfather's recovery "flies in the face of those who have been busy spreading lies that Madiba is in a 'vegetative state' and just waiting for his support machines to be switched off," he said, using his grandfather's clan name.
The oldest Mandela grandson, who is chief of Mandela's birth place Mvezo in the rural Eastern Cape province, has fallen out with relatives after moving the three graves of Mandela's children without consulting the family.
Following a court order, the remains were reburied earlier this month in Mandela's childhood village of Qunu, where the anti-apartheid hero has said he himself wishes to be buried after his death.
Mandla's family has laid a charge of grave-tampering against him, and Mandla is appealing the court ruling.
Mandla was notably absent for Mandela's birthday celebrations in hospital last Thursday.
Mandla was instead carrying out community projects around his village as part of Mandela Day, a global day of charitable acts in honour of his grandfather, seen as the democratic father of South Africa.
Mandela's current hospital stay is his longest since he was released from prison in 1990, after serving 27 years under the apartheid regime.