JOHANNESBURG—South African officials may block the Dalai Lama from celebrating the 80th birthday of his friend and fellow Nobel Peace Laureate, Archbishop Desmond Tutu, amid fears that Chinese pressure is trumping the country’s much-vaunted policies on freedom of speech and human rights.

South African newspapers are already drawing parallels between the situations of Tibetans under Chinese rule and black South Africans under the racist apartheid regime that ended in 1994. The tensions over the Dalai Lama’s visa application also are a sign of how powerful China’s influence has grown in Africa.