She said 50,000 women are estimated to be losing their jobs while on maternity leave each year, according to Labour Party analysis.
Labour claims an average family with a newborn baby is losing £2,000 as a result of cuts to tax credits, maternity pay and support for new families.
It also claimed the Government is making it easier for employers to discriminate against women during maternity leave by charging £1,200 to take a maternity discrimination case to employment tribunal.
Cooper's comments come as Labour is set to launch a consultation on a new deal for working mothers. It aims to find out the impact of cuts to maternity pay and support for families, as well as the living standards of young families.
Hidden outrage
Cooper called the discrimination against working mothers a "hidden outrage" and a complete waste for the economy.
"New mums are being betrayed by the Government," she said. "They face a triple whammy from maternity discrimination made easier by ministers, big cuts to family support and the cost of living with a new baby is far outstripping wages."
"We know David Cameron has a problem with women. This is now resulting in him failing new families."
Research last month from law firm Slater Gordon found many workers felt frustrated when returning to work, and a fifth said they felt less valued in the workplace.
Cooper said: "We need a new deal for new mums that shows motherhood is valued, and that recognises the vital role parents play in the economy as well as in the home."
Earlier this year the Government introduced shared parental leave and pay. From April 2015, couples can choose how they share childcare in the first year after birth.
