More than 85,000 people attended the service at the FNB stadium near Johannesburg and millions more witnessed it across the globe.
The Shlokas were recited by Pundit Ashwin Trikamjee, who is the President of the South African Hindu Maha Sabha.
"It was a special privilege to have been called upon to represent the Hindu community at the memorial service," Trikamjee, who has also led Hindu prayers at the inaugurations of both former President Thabo Mbeki and President Jacob Zuma, said.
"It was an honour at both the inaugurations, but this one was even more special, as it was for the man who brought not only freedom to all South Africans, but also played a major role in bringing together religious groupings across the board to find ways of improving the moral and social fabric of society," Trikamjee said.
The Hindu prayer at Mandela's inauguration was done by late Pranlal Lakhani as the country entered a new era with a new constitution that recognised the freedom of religion for all.
It has been the practice since then for all major government events to commence with prayers by representatives from the largest religious communities in South Africa.
At the memorial service today, the Muslim community was represented by Moulana Ebrahim Bham of the Jamiatul Ulema of South Africa (Council of Muslim Theologians).
The Jewish community was represented by Chief Rabbi Warren Goldstein and the Christian community by Archbishop Thabo Makgoba.
Mandela, South Africa's first black president who steered his nation out of apartheid and into multi race democracy, died late on Thursday at the age of 95 after protracted illness.