A sharp increase in air fares, due to the earlier timing of Easter, was the main reason behind the rise from February's rate of 0.3%, the ONS said.
Inflation is now at its highest level since December 2014, but it remains below the Bank of England's 2% target.
The Bank has said that it expects inflation to stay below 1% this year.
Continuing low inflation makes the chance of an interest rate rise in the near future unlikely.
Air fares jumped by 22.9% between February and March, reflecting the earlier timing of Easter compared with last year. This, alongside, a rise in clothing and footwear prices, was the main reason for March's increase.
However, this was partially offset by a fall in food prices and a smaller rise in petrol prices compared with March last year.
Under the separate Retail Prices Index (RPI) measure, which includes housing costs, inflation was 1.6% in March, up from 1.3% in February.
UK inflation as measured by the Consumer Prices Index rose to 0.5% in March, according to the Office for National Statistics (ONS).