The party said the figure represents how much the tax and benefit changes could cost a family with one child and another on the way.
It is the latest suggestion that poorer working families, and especially women, are getting the toughest deal from the Coalition's austerity policies.
Labour calculated that working parents with one child would have their household budgets squeezed by an average of £688 next year and then by another £1041 a year later when they have a second baby.
It worked out the figure by adding up cuts to child tax credits, the three-year freeze on child benefit, the 1% cap on the rise in statutory maternity pay and the abolition of the maternity grant.
It said the figures had been adjusted to allow for Government moves to raise the tax allowance for parents.
The changes come on top of the loss of £1500 in childcare tax credits for a single parent with two children.
Stephen Twigg, the Shadow Education Secretary, said: "This will be a major blow to working parents. "At a time when they are already facing rising bills, including inflation-busting hikes in childcare costs, they are now being hit by David Cameron's toddler tax.
"Instead of punishing mums who go out to work, we need to ensure that we provide affordable and quality childcare.
"That would be good for parents and also good for the economy – a quarter of unemployed parents say the cost of childcare is putting them off going back to work.
"Instead of threatening the affordability and quality of childcare, we need to examine best practice from Scandinavia, which provides funding for high-quality nursery provision and the rate of female employment is higher."
The SNP shares Labour's concerns over the impact of benefit and tax changes on working women.
Linda Fabiani MSP, a member of the Scottish Parliament's Welfare Reform Committee, said: "This is yet more damning evidence of the Tories' ideological crusade against hard-working people who need their household budgets protected the most.
"Having recently capped benefit increases – effectively cutting them in real terms – the Tories are making life more and more difficult for low-income families, particularly when you factor in rising energy bills, rising petrol prices and rising food costs.
"Decisions over taxes and welfare in Scotland should be made by people in Scotland, which is one of the most compelling arguments for a Yes vote in 2014."
John Dickie, of the Child Poverty Action Group, said: "There is no doubt that current UK tax and benefits policies are hitting the poorest families hardest."
Last year, the Institute for Fiscal Studies calculated that the poorest working families could see their annual income fall by nearly £4000 because of changes to the tax credit regime.
The Department of Work and Pensions defended below-inflation increases in benefits.
A Government spokeswoman said: "In difficult economic times, we've protected the benefits of disabled people and pensioners who have little means to increase their income.
"We've also committed to helping people who claim working-age benefits and tax credits and will increase this support by 1%. This was a tough decision, but it will ensure that the welfare budget is sustainable over the longer term and will continue to help the people who need it most."