Up to 3.5 million people will be eligible for a £1,200 bonus on their savings under plans announced ahead of the Budget.
The new Help to Save accounts, which will be launched within the next two years, aim to give low-paid workers a hand to build their rainy-day funds.
Consumer champion Martin Lewis has warned some people could be encouraged to put money into the scheme when in reality they would be better off clearing their debts.
Details of the accounts were set out by Prime Minister David Cameron earlier this week.
They will allow those in work and receiving universal credit or working tax credits to save up to £50 a month and receive a 50% bonus after two years, worth up to £600.
Account holders can then choose to continue saving for a further two years and receive another £600 bonus.
This means a low-paid worker will be able to build a £3,600 savings pot after four years - with £1,200 of the pot coming from the Government.
David Haigh, financial capability director for the Money Advice Service (MAS), said its research has shown four in 10 adults have less then £500 in savings.
The Government plans to consult shortly after the Budget on details of how the policy will work. It said the accounts will be available no later than April 2018.
People will be able to make withdrawals while they have money in the account to cover urgent costs and there will be no restrictions on how Help to Save cash can be used, the Government has said.
Mr Lewis, founder of MoneySavingExpert.com, said: "Already, many people make the mistake of trying to save when they are in debt and yet the cost of debt for most usually vastly outweighs the gain of saving.
"My worry with Help to Save - especially because of the long delay before people get the bonus - is that people may start to think that everyone should put aside money each month, when the truth is for many with expensive debts, especially payday loans, that's a bad idea."
Mike O'Connor, chief executive of StepChange Debt Charity, said: "To build financial resilience and to protect people on low-incomes from the risk of falling into debt, any savings scheme needs to work alongside other elements of a responsive safety net, including access to more sustainable and affordable credit and better protections for those in financial difficulty."
Danny Cox, chartered financial planner at Hargreaves Lansdown, said: "Instilling the savings habit is not just about attractive products with low minimum contributions, there needs to be education programmes alongside to promote the benefits of saving."
Mark Lyonette, chief executive of the Association of British Credit Unions, said: "Credit unions have years of experience helping people to save and make the most of their money - whether by working with employers to let staff save direct from payroll, letting people tuck away savings alongside their loan repayments, or helping people plan and afford expenses like Christmas, weddings and holidays - so many credit unions will be keen to provide the new Help to Save accounts."
Shadow work and pensions secretary Owen Smith claimed benefits cuts will leave families struggling to make it to the end of the week, "let alone save for the future".
He has said of the new Help to Save scheme: "This is like stealing someone's car and offering them a lift to the bus stop."