A stampede by fans during a warm-up match between Nigeria and North Korea on Sunday left 15 people injured.
"The government will not tolerate any unruly, disruptive and unsafe behaviour that impacts negatively on those attending public events," government spokesman Themba Maseko said in a statement on Wednesday.
Maseko urged fans not to enter stadiums during the World Cup without valid tickets.
"Those found in possession of illegal tickets will be prosecuted," he said.
The South African government has taken pains to assure foreign visitors that they will be safe during the month-long tournament, which starts on Friday.
Security has been one of the biggest issues ahead of the World Cup because of South Africa's high rate of violent crime - with 50 murders a day, almost the same rate as the United States which has six times the population.
The country's crime rate is among factors blamed for lower-than-expected foreign bookings to attend the World Cup.
The government and local organisers have insisted fans will be protected by a $174 million security plan including more than 40,000 specially deployed police.
Meanwhile, South Africa's Finance Minister Pravin Gordhan has warned local government authorities and state-owned companies not to use state funds to buy World Cup tickets for officials.
In a written reply to a question in parliament, Gordhan said the National Treasury issued a circular after it received information that certain local governments planned to buy tickets and T-shirts for councillors and officials ahead of the month-long sports event which starts on Friday.
Gordhan said in the reply such spending falls under "irregular ... and fruitless and wasteful expenditure".
South Africa's budget deficit stood at 6.7 percent of GDP in the 2009/10 financial year and the government plans to cut it to around 4 percent by 2012/13.
