Tutu also accused South Africa of betraying its legacy of struggling against apartheid by failing to take action against Mugabe.
While regional countries such as Botswana and Zambia have taken a tough line against Harare, the South African government has stopped short of calling on him to resign.
South Africa had strong historic links with Mugabe, who provided support during the struggle against apartheid.
Tutu's comments come as a high court judge in Zimbabwe ordered a group of detained human rights activists be taken to hospital in order to investigate allegations of torture.
Jestina Mukoko, a leading human rights activist, and six others have been charged with plotting to overthrow the Zimbabwean government.
A human rights lawyers said on Wednesday that a judge ordered Mukoko and six other activists be sent to hospital under police guard.
Beatrice Mtetwa told the Associated Press the seven activists would be brought to court again on Monday to determine the next steps in the case.
Mukoko, a former newscaster who headed the Zimbabwe Peace Project, was taken away at gunpoint in Harare on December 3 by unidentified men.
If found guilty of the charges, the activists could face the death penalty, lawyers have said.
Zimbabwe police officials have denied holding Mukoko, who had not been seen since being taken from her home on the same day as nationwide protests against the country's deepening economic and health crises.
The case has added to doubts over the implementation of a power-sharing agreement between Mugabe and opposition leader Morgan Tsvangirai, seen as a chance of rescuing the once relatively prosperous country from economic collapse.
The pact was formed in September, but has unravelled due to a fight over control of important ministries.
Amid the political stalemate, Zimbabweans continue to sink deeper into poverty, and more than 1,000 people have died from a cholera epidemic that threatens to spread to neighbouring South Africa.