Queues began on Wednesday afternoon and frustration built as people inched forwards for a chance to get tickets, including some for the final on July 11.
Computer crashes tested the patience of crowds at some centres and tempers flared.
"Police were called in," said Eugene Opperman, South African Police Services spokesman in Gauteng of an incident at Brooklyn Mall in Pretoria where local radio reported that pepper spray was used to restore order.
"There was pushing and shoving among the people and it was decided police should go there for crowd control," added Opperman.
In Sandton, north of Johannesburg, angry South Africans argued with police who used a vehicle to disperse the crowd.
A 64-year-old man suffered an apparent seizure as he waited in a queue in Cape Town, police said.
FIFA said in a statement that 1,610 tickets were sold at ticketing centres within an hour of counters opening while another 2,166 were bought at banks.
World football's governing body acknowledged the huge demand had resulted in delays in issuing tickets.
Some banks were not able to process applications when systems crashed, leading to anger and frustration among fans.
"That's it, I've had enough of this," said Glen Watson, a 43-year-old South African who had queued outside a bank in Sandton for four hours.
Around 120,000 of the tickets are available to South Africans for $20, the lowest price at a World Cup for many years.
Ticket sales in the country had been below expectations until recently and FIFA was criticised for selling them in a complex system over the internet which was alien to poor fans accustomed to getting tickets for cash on match days.
Officials acknowledged mistakes had been made and launched a new system of sales through ticketing offices and supermarkets on Thursday, hoping to sell out the tournament after disappointing overseas sales and returned tickets.
MANDELA VOTE
"I'm going to kiss my ticket when I get it," said one man called Godfrey at the Maponya Mall in South Africa's biggest black township, Soweto. He did not want to give his name because he was skipping work to queue.
"The last time I waited in a line like this was when I voted for Mandela," he said, recalling the elections won by Nelson Mandela at the end of apartheid in 1994.
FIFA had previously said the final was sold out but on Wednesday announced another 300 tickets would be released for the biggest match in world football.
"I'm just waiting in anticipation," said Marlin Fisher, training to be a church minister. "I would love for South Africa to go all the way and I will also put my money on the Brazilian team."
Tickets are much higher than normal prices for top-level football in South Africa.
Even the special cheap tickets are more than five times the cost of normal top-class games, with costs escalating drastical
