President Jacob Zuma said Alexander would be remembered for his "pioneering work" on language policy.
"We are saddened by this tragic loss of a South African who had contributed selflessly to the struggle for liberation and to building a better society and a better South Africa," Zuma said in a statement.
"The country has lost a person of high intellectual and academic standing. We extend our deepest condolences to Dr Alexander's family, relatives and friends."
The ANC said Alexander was "a courageous leader, who was outspoken in his opposition to the apartheid administration".
"He made his mark in the collective history of our struggle. His role in the broader liberation movement will always be remembered," ANC spokesperson Jackson Mthembu said in a statement.
The Nelson Mandela Centre of Memory said the former president had considered Alexander "a hero of the struggle".
"Neville Alexander has made an invaluable contribution to our country's cultural and political life," said the centre's CEO Achmat Dangor.
Democratic Alliance MP Annelie Lotriet said the party was saddened at Alexander's death.
"Professor Alexander will be remembered for having played an instrumental role both in standing up against the apartheid state and fighting for equal education, a fight which continues today," she said.
"Alexander made a remarkable and selfless intellectual contribution to liberty in South Africa. The DA will continue to fly the flag of liberation through education. It is a legacy well worth fighting for."
Arts and Culture Minister Paul Mashatile said Alexander had always argued that languages, especially African ones, were instrumental in upholding human dignity.
"He occupied a formidable space in South Africa's intellectual, political and cultural life and he was also an activist of note throughout his life," Mashatile said in a statement.
"He was a great proponent of multilingualism in general and especially in education."
The 75-year-old died at his home in Grassy Park, on the Cape Flats, on Monday.
University of the Free State vice-chancellor Jonathan Jansen told SABC news that Alexander had been diagnosed with cancer several months ago.
Alexander was one of the founders of the National Liberation Front. He was convicted in 1964 of conspiracy to commit sabotage and was sent to Robben Island for 10 years. During his incarceration, he taught history to fellow inmates.
According to SA History Online, Alexander wrote of his time in prison: "The 'University of Robben Island' was one of the best universities in the country. It also showed me that you don't need professors." – Sapa