Former Zambian president Kenneth Kaunda was among the few invited guests at a private gathering where his grandchildren presented Mandela with a three-tier cake and sang "Happy Birthday, dear Granddad", his office said.
"He is very well ... he is healthy and taking into account the kind of life he had, it is really heartening ... he is getting old, he is getting frail but he is absolutely healthy, full of life, spirits high," Mandela's wife Graca Machel told BBC.
"We will gather at home, we will sit around, give him a lot of love," Machel said.
Sunday was also the first annual Nelson Mandela International Day, declared by the United Nations.
For the occasion, ordinary people in South Africa and abroad committed themselves to devoting 67 minutes of their time to community service, to mark the number of years Mandela spent in politics, an initiative backed by global figures like former US president Jimmy Carter and Martti Ahtisaari of Finland.
"I encourage us all to heed the call to engage in some form of service to others, in honour of the 67 years of sacrifice and service Madiba gave to us," said Obama, referring to South Africa's first black president by his nickname.
A group of 30 bikers including Hollywood actor Morgan Freeman undertook a road-trip from Johannesburg to Cape Town, engaging in community projects along the way such as building a fence at an AIDS centre at an impoverished township.
"I take it as my connection to Madiba. We should do it everyday," said Freeman, who played Mandela in the movie "Invictus".
The UN celebrated with activities around the world from Zambia in Africa to Kazakhstan in Central Asia.
Communities in Sudan were to participate in a "Football for Peace" tournament in El-Fasher, with the winning team awarded the Nelson Mandela Cup.
In Spain a 6.7-kilometre (nearly 15-mile) charity walk in Madrid was held late Sunday.
And in Vienna, on the sidelines of the 18th International AIDS Conference, South African Deputy President Kgalema Motlanthe led dozens of delegates in a chorus of "Happy Birthday, Madiba" accompanied by the sound of vuvuzelas.
"Nelson Mandela is a towering figure. He embodies the highest values of humanity, and of the United Nations," said UN Secretary General Ban Ki-moon.
"Nelson Mandela’s accomplishments came at great personal cost to himself and his family. Today, on the first Nelson Mandela International Day, we thank him for everything he has done for freedom, for justice and for democracy," said Ban.
Neighbours gathered outside the high perimetre walls of Mandela's Johannesburg home, some clutching "Happy Birthday, Madiba" signs, but went away disappointed after police relayed the family's request for privacy.
Thousands turned out to celebrate at Mandela's birthplace in Mvezo, hundreds of miles away in the Eastern Cape, where President Jacob Zuma described Mandela as a symbol of unity and tolerance.
"Of all the things that Madiba cherishes up to this day, it is the love of all humanity, freedom, justice and compassion for all people," said Zuma.
Jailed for 27 years by the country's white minority government for resisting apartheid rule, Mandela was released in 1990 and led negotiations with the government that culminated in his election as the country's first black president in 1994.
He stepped down in 1999, after serving one term in office. He has made few public appearances since he retired from public life in 2004.