This was 0.5 of a percentage point higher than the corresponding annual rate of 5% in August, the agency said in a report.
The CPI measures changes in the price level of consumer goods and services purchased by households.
September's CPI was within the South African Reserve Bank's inflation target range of between 3% and 6%.
The rising inflation rate was influenced by food inflation which increased by 5.8% year-on-year in September from 4.9% in August.
Transport inflation was also high, increasing to an annual rate of 6.6% in September, compared to 4.9% in August.
The petrol price increased by 93 cents a litre in September. – Sapa.