Riah Phiyega said police had been forced to shoot after armed protesters charged them, "firing shots", at the Marikana mine in the north-east.
At least 78 people were injured in the confrontation, she added.
Unions are demanding an inquiry into the incident - one of the bloodiest police operations since apartheid.
The Lonmin-owned platinum mine has been at the centre of a violent pay dispute, exacerbated by tensions between two rival trade unions.
Violence had already killed 10 people, including two police officers, since the strike began a week ago. Read More