Tutu, who as the archbishop of Cape Town in the 1980s and 1990s waged an outspoken campaign against the apartheid regime, called on South Africans to express their solidarity with their northern neighbours.
If you could have more people saying I'll fast maybe one day a week just to identify myself with my sisters and brothers in Zimbabwe, Tutu, who fasts once a week, said on Talk Radio 702.
International rights group Civicus said it planned to launch a similar campaign within two weeks.
We're expecting several hundred South Africans to join for one, two, three, four days or more, said spokesman Kumi Naidoo .
The group is also planning demonstrations in front of the Zimbabwean embassy to put pressure on the South African government, he added.
Civicus called on the government to speak out against what it described as the violence of Zimbabwean President Robert Mugabe and his government.
Tutu has also criticised South Africa for its refusal to take a harder line on Mugabe.
In a December 24 interview with the BBC, he said he was ashamed of his government's failure to stand up to Mugabe, describing it as a betrayal of the ANC's anti-apartheid legacy.
Under Mugabe, Zimbabwe is battling a cholera epidemic, hyper-inflation, severe food shortages and chronic political instability. – The Times
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