Prices rose by 6.7% in the year to March, up from 5.6% in the year to February.
It represents the highest rate of inflation since November 2000.
CSO figures show the largest increase in prices in the 12 months to March were in transport, up over 18%, and housing, electricity and gas, up over 17%.
The cost of alcohol went up by 7% in the same period.
The monthly increase in prices between February and March this year was 1.9%, representing the largest monthly increase since 1997.
