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.
"Those found in possession of illegal tickets will be prosecuted," he said.
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.
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.
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.
