Mr Kathrada was among those tried and jailed alongside Mandela in the Rivonia trial in 1964, which drew worldwide attention and highlighted the brutal legal system under the apartheid regime.
He died in hospital in Johannesburg after a short illness following brain surgery.
Mr Kathrada spent 26 years and three months in prison, 18 of which were on Robben Island.
After the end of apartheid, he served from 1994 to 1999 as parliamentary counsellor to President Mandela in the first African National Congress (ANC) government.
"This is great loss to the ANC, the broader liberation movement and South Africa as a whole," Neeshan Balton, head of the Ahmed Kathrada Foundation, said in a statement.
"'Kathy' was an inspiration to millions in different parts of the world."
His activism against the white-minority apartheid regime started at the age of 17, when he was one of 2,000 "passive resisters" arrested in 1946 for defying laws that discriminated against Indian South Africans.
'A determined revolutionary'
The ANC was banned in 1960, and two years later Mr Kathrada was placed under "house arrest".
Soon afterwards, he went underground to continue the struggle as a member of the ANC's armed wing, Umkhonto we Sizwe (MK).
In July 1963, the police swooped on Liliesleaf Farm in Rivonia, a Johannesburg suburb where Mr Kathrada and other senior activists had been meeting in secret.
At the famous Rivonia trial, eight of the accused were sentenced to life imprisonment with hard labour on Robben Island.
His fellow prisoners included Mandela, Walter Sisulu and Denis Goldberg.
Derek Hanekom, a fellow veteran activist and now a government minister, said he had lost a "revolutionary mentor and dear friend".
"Comrade Kathy was a gentle, humane and humble soul. He was a determined revolutionary who gave his entire life to the liberation struggle in our country," Hanekom said.
Fellow Robben Island prisoner Laloo "Isu" Chiba said Mr Kathrada was a moral figurehead of the anti-apartheid movement.
"He has been my strength in prison, my guide in political life and my pillar of strength in the most difficult moments of my life. Now he is gone," Chiba, 89, said in a statement from the foundation.
While in prison, Mr Kathrada obtained four university degrees.
He will be buried according to Muslim religious rights, his charity foundation said.