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City authorities had said earlier that the park, which is hosting a day-night "Welcome the World Concert", would close the gates when it reached capacity at 17 000.
A line of police were deployed to bar entry at dusk.
However, hundreds of people were still massed at the barriers.
The crowd was entertained from early afternoon by musical acts including Nomfusi and the Lucky Charms, Ernie Ulster and DJ Reddy D.
One of the performers in the second half of the concert on Thursday evening will be rhythm and blues star R Kelly, accompanied by The Soweto Spiritual Singers.
Earlier fans were requested to avoid the area on the Grand Parade and rather go to Adderley Street, where giant television screens had been erected.
The reported injuries were apparently all minor.Motorists on the city’s surrounding highways were also asked via new electronic boards to stay away from the CBD because of congestion.