Earlier this month, Kathrada, 87, underwent surgery at a Johannesburg hospital to remove a clot on his brain.
Since then, he has experienced several post-operation complications.
"Kathrada has contracted pneumonia, which has affected both his lungs," Ahmed Kathrada Foundation director Neeshan Balton said.
"Despite appropriate medical care, his condition is deteriorating. He is currently comfortable."
Balton said the foundation would keep the public updated on Kathrada's condition, including on Twitter. The foundation's twitter handle is @KathradaFound.
Kathrada, along with Andrew Mlangeni and Denis Goldberg, are the last three of the Rivonia trialists still alive following Nelson Mandela's death in 2013. Mandela and Kathrada were close friends while imprisoned on Robben Island.