Speaking at an event honouring Mandela in Cape Town on Saturday, mayor Patricia de Lille said it was an attempt to combat cynicism.
South Africans were never "truly convinced that someone could put the interests of others first without some selfish goal in mind", she said.
People should heed the call to take 67 minutes of their time to help others because Mandela "had taught us . that you can still be a hero and change the world".
According to the Nelson Mandela Foundation, there are more than 160 streets, highways, parks, squares and buildings named after Mandela. He has received more than 1000 awards, including 115 honorary degrees.
Mandela is spending his birthday in his home town of Qunu, Eastern Cape.
A number of cabinet ministers are in the area, opting to do their 67 minutes of community work close to where the elder statesman will be spending the day.
Police Minister Nathi Mthethwa, who is also acting Co-operative Governance minister, will be working at a police station in Mthatha, and cleaning and painting a school.
Defence Minister Lindiwe Sisulu is also painting a school that has been converted into a community hall in Mthatha.
Yesterday, 50 street children and youngsters from orphanages were given breakfast at Mthatha's city hall by mayor of King Sabata Dalindyebo municipality, Nonkoliso Ngqongwa.
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