It says the rise is a product of problems with the UK's welfare system – not just the pandemic and cost of living crisis.
The charity, the country's leading operator of food banks, distributes millions of food parcels to those in need every year – and the number has risen again this year.
Figures from the Trussell Trust show 5,152 food parcels were handed out in Monmouthshire in the year to March in the area's four distribution centres – more than double the 3,898 in 2021-22.
This was the highest number of parcels provided in the area since at least 2017-18.
Last year 1,690 of these parcels – 33% – were given to children. In 2021-22 this figure was 1,275 (33%).
Across the UK, a total of 2,986,203 emergency food parcels were given out between April 2022 and March this year – up 37% on the year before.
These figures cover parcels handed out by the Trussell Trust itself, but do not include emergency food supplies provided by other charities and organisations.
Emma Revie, chief executive at the Trussell Trust, called the statistics "extremely concerning".
She said: "The continued increase in parcel numbers over the last five years indicates that it is ongoing low levels of income and a social security system that isn’t fit for purpose that are forcing more people to need food banks, rather than just the recent cost of living crisis or the Covid-19 pandemic."
“Food banks were set up to provide short-term support to people in an emergency, they are not a lasting solution to hunger and poverty, and more than three quarters of the UK population agree with us that they should not need to exist," she added.
Along with the Joseph Rowntree Foundation, an anti-poverty charity, the Trussell Trust is urging the Government to adopt an 'essentials guarantee', ensuring Universal Credit payments always cover the cost of basic essentials.
Research by the two charities suggests the current £85 Universal Credit standard allowance is £35 short of this target.
“For too long people have been going without because social security payments do not reflect life’s essential costs and people are being pushed deeper into hardship as a result," Ms Revie added.
Across Wales, 185,320 parcels were handed out in the year to March – up 41% from 131,663 the year before, and the largest increase of any of the UK's four home nations.
A Department for Work and Pensions spokesperson said: “We are committed to eradicating poverty and we recognise the pressures of the rising cost of living, which is why we have uprated benefits by 10.1% as well as making an unprecedented increase to the National Living Wage this month.
“This is on top of changes already made to Universal Credit which mean claimants can keep more of their hard-earned money – a boost worth £1,000 a year on average."
“We are also providing record levels of direct financial support for the most vulnerable,” they added.