The stampede was triggered mostly by Nigeria supporters, holding what police said were photocopies of tickets, trying to push their way into the 10,000-seater Makhulong stadium after the game had started, a witness said.
The incident marred a day when more fans and teams flew in to South Africa, which hosts the month-long football jamboree, the world's most watched sporting event, from Friday (June 11).
It is the first time the 80-year-old tournament has been held in the continent.
The police officer sustained serious injuries when fans pushed the gate on to him in their effort to enter the stadium to watch the match between the two World Cup participants.
There was no immediate word about his condition.
"He was crushed by the gates as people stormed them, trying to get in," a police official at the scene informed.
Nigeria won the match 3-1.
A statement from the sport's governing body, FIFA, stressed that the match was not staged under its auspices and said it was still "fully confident" about its organisation for the World Cup.
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