In its Cost of a Child in 2017 report, the charity says the cost of raising a child to the age of 18 for a two-parent family, excluding housing, childcare and council tax has risen to Â£75,436.
A couple earning the National Living Wage falls 13% short of that, it said.
Costs are up 4% compared with 2016.
The figures for 2017 reflect rising prices - especially of public and private transport - but it is cuts to some welfare benefits and the failure to up-rate others that is causing the pinch to be so severe for low income families, the report says.
"For the first time in post-war history, these cost increases are not being matched by increases in support given to families from the state," said report author Donald Hirsch, Director of the Centre for Research in Social Policy at Loughborough University.
He predicted the problem would become steadily worse.
Two parents earning the National Living Wage of Â£7.50 an hour would fall 13% short of the income needed to provide a child with a "no-frills living standard", says the CPAG.
The total includes food, clothing, heating as well as buying birthday presents and a week's self-catering holiday in the UK the charity said.
A lone parent working full-time on the National Living Wage would fall short by 18%, according to the report.
"Families unable to cover their costs on benefits must either undergo serious hardship, fall back on the help of their families or go into debt," the report concludes.
Child benefit and child tax credit rates have not increased since 2015 and other cuts to welfare, including the benefit cap and the limiting of child tax credit entitlement to two children per family, are affecting the income of some families.
The CPAG provides an annual assessment of the cost of raising a child based on the "minimum income standard" or a very basic level of provision. This is determined through in-depth discussions with members of the public, asking them what it is essential for a child to have.
However the charity says that "years of austerity have reduced public expectations of what constitutes essential spending."
Higher inflation and a freeze on state benefits mean low-income parents cannot meet the basic costs of raising a child, according to the Child Poverty Action Group.