The match was stopped for around five minutes early in the second half because of the injuries and safety of the fans in the overcrowded main stand where the fencing had been removed.
"There are 14 people slightly injured and one policeman seriously injured," South African police official Eugene Opperran said.
He said the stampede started when too many fans had obtained free tickets for the match and stormed the entrance to the stadium.
Hundreds of mostly Nigerian fans pushed the gate on to the police officer in their effort to enter the 10,000-seater stadium to watch the match between the two World Cup participants.
"He was crushed by the gates as people stormed them, trying to get in," another police official at the scene told Reuters.
He said many of the fans had what appeared to be just photocopies of the tickets.
Among those injured were two children, according to a Reuters witness.
Some 500 fans remained in the area around the stadium for some time after the stampede before dispersing peacefully.
The sport's governing body FIFA said in a statement that they did not have any concerns about a repeat incident occurring during the World Cup, which starts on Friday.
"FIFA would like to reiterate that this friendly match has no relation whatsoever with the operational organisation of the 2010 World Cup, for which we remain fully confident," the statement read.
"FIFA had nothing to do with the ticketing of this game."
Inside the stadium there were still many empty seats as the match was not sold out.
"Nobody can be blamed for this. We did not have any choice of an alternate bigger venue," Nigerian Football Federation board member Taiwo Ogunjobi said.
"We are just thankful nobody died. The tickets were free and too many people wanted to get in." The stadium in the Johannesburg suburb will not host any World Cup matches.
There was no immediate word on the policeman's condition.
Nigeria won the match 3-1, taking a 17th minute lead through Yakubu Aiyegbeni after a series of swift passes through the centre of the Korean defence.
A penalty converted by Victor Obinna on the hour doubled the score but the North Koreans pulled one back within a minute.
Elderson Echiejile's errant back pass was intercepted by Jong Tae-se, who scored from close range.
A sparkling run and cut inside from Kalu Uche three minutes from time saw substitute Obafemi Martins score a third for the Nigerians.
Cha Jong-hyok was sent off with 13 minutes remaining after collecting a second yellow card.
After successive draws against Saudi Arabia and Colombia, it was the first win for the Nigerians under new coach Lars Lagerback.
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