The men, part of a group of 80 supporters who had travelled from South America via Angola, were identified as members of the notorious "Barrabravas" gang and were on an entry blacklist for the tournament, which starts on June 11.
Police said at least two were Barrabravas leaders and a third was out on bail for murder.
"Intelligence indicated that these persons would commit acts of public disorder, engage in acts of violence and provoke conflict with certain fans of opponent teams and other groups from Argentina," a police statement said.
"They were immediately intercepted and refused entry into the country."
South African police have little experience of football hooliganism, which does not occur at domestic games, and are relying on foreign forces as their eyes and ears in picking up potential trouble-makers.
The statement trumpeted the arrests as a "groundbreaking move" that showed that months of liaison between police forces across the world was paying off, and that "loutish and violent behaviour" would not be tolerated at Africa's first World Cup.
South African police minister Nathi Mthethwa said last month local and British police had thwarted an attempt by English hooligans to get to the World Cup via Dubai.
As many as 3,200 known English trouble-makers had been told to surrender their passports to prevent them travelling, he said.
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