"What we are seeing with the Zuma/Thabo Mbeki debacle is less than dignified," he told an Institute for Justice and Reconciliation symposium in Cape Town.
"I think we can do better. Beware also the law of unintended consequences. Things may just snap."
He said he thought the ANC needed to give better guidance to the nation about its transition and succession policies.
The party leadership needed to pause and "just go back, take stock and ask 'how did we get here'?"
"How do people burn a T-shirt with Thabo Mbeki's face on it on behalf of Zuma? I don't understand. I've known both of them for 30 years.
"I think we need to provide, as the ANC... a better, far more dignified way of doing things. This is not the way. It unsettles people."
SA will rise or fall on issue of local government
Sexwale said South Africa was going to "rise or fall" on the issue of local government.
It did not matter how good the country looked at the level of national leadership; the issue would come down to the level of people responsible for delivery on the ground.
It was disturbing to see the way people were trashing their own cities.
"People are getting increasingly uncomfortable, and they are saying 'delivery, delivery, delivery' on the ground. I think that's where this thing will catch us."
He said that the auditor-general had qualified all but four of the reports on municipalities' finances that he most recently submitted to parliament, and had spoken about maladministration, misappropriation, fraud, corruption and underspending.
"We have made a mistake in the ANC," Sexwale said. "It was a mistake for us to take everybody down to Cape Town and to Pretoria. Your best generals go to the worst front. In mining, your best engineers, technicians, they go to the rockface.
"We haven't done so and a quick corrective action is required otherwise that's where this nation may face a crisis."
Service delivery facing skills problem - De Klerk
Speaking at the same symposium, former president FW de Klerk said the problem with service delivery was generally not a lack of resources, but a lack of skills, planning and management.
Effective municipal, health and social welfare services would significantly help to address the plight of the poorest South Africans.
"Municipalities have a key role to play in the war on poverty and they are not playing that role successfully in all too-high a percentage of cases," he said.
De Klerk said no-one could quarrel with the underlying goals of black economic empowerment but the question was how these ideals could best be achieved in the real world.
Experience taught that economic outcomes could not be determined by legislation or compulsion. More often the result of such attempts was the opposite of their authors' intention.
He feared it would be the same with BEE legislation.
"How can the state determine ownership levels on an ethnic basis in an open market economy? How can we achieve BEE's objective of equitably transferring ownership from whites to blacks without undermining property rights?"
Real empowerment meant enabling people to acquire the skills,
opportunities and resources they needed to add value and compete
successfully in a tough and competitive world, De Klerk said.
Sapa