The average price of diesel rose 18.1% and petrol increased by 7.7% last month.
The CSO said the rate of inflation increased by 3.6% in the last 12 months, which was in line with an estimate published last week, amd the highest level in more than two years.
But it was significantly higher from the rate of inflation in the 12 months to February which was 2.7%.
Transport costs increased 5.2% on the month, with Housing, Water, Electricity, Gas and Other Fuels up by 3.9%, today's figures show.
The CSO said the national average price of diesel in March was €2.05 - an increase of 31 cent per litre compared with February.
The average price of petrol was €1.88 last month - up 13 cent in the month.
"Diesel and petrol contributed 0.27 and 0.11 percentage points towards the overall inflation rate in March, respectively," it added.
Professor Lisa Ryan from UCD said that heating oil is mainly derived from kerosene which is traded internationally with aviation fuel.
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She said they are "two different markets," and households in Ireland, along with the UK, are "very reliant" on heating oil compared with other countries.
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