The scheme, which sees the government cover 20 per cent of working parents' childcare costs, is already available to families of children under four and was due to be extended to families with under-12s and disabled children under 17 years old by the end of this year.
However, HM Revenue & Customs' childcare service website, which families use to register for tax-free childcare, has been beset with IT glitches. The Treasury has announced the full rollout will now take place in March 2018 in order to address any website issues.
In a statement to parliament, Treasury minister Mel Stride said the government will now phase in the extension of tax-free childcare between now and March, starting with the scheme opening up to families with children under six on 24 November.
"Over the summer some parents did not receive the intended level of service while using the site," he said.
"While the majority of parents used the childcare service without significant problems, some parents experienced technical issues including delayed decisions about their eligibility."
"Over the coming months, we will gradually open the childcare service to parents of older children, while continuing to make further improvements to the system.
"This means we can manage the volume of applications going through the service, so parents continue to receive a better experience and prompt eligibility responses when they apply."
Stride added that applications for tax-free childcare were "lower than expected" and so the government plans to do more to promote it.
Neil Leitch, chief executive of the Pre-school Learning Alliance, said the delay was unsurprising given the problems with the childcare services website.
"With the childcare service system now set to service a significantly higher number of parents, it is vital that the government invests what's needed to deliver and maintain an IT system that both parents and childcare providers are able to use and rely on," he said.
Purnima Tanuku, chief executive of the National Day Nurseries Association (NDNA), said the delay will be "disappointing" for families who hoped to access the scheme earlier but backed the delay.
"We feel this is a sensible approach in order to avoid repeating the chaos we saw in the summer when parents were registering on the same website for their child's 30 hours funded childcare place," she said.
"A straw poll NDNA held in September revealed that four in five nurseries had spent time helping parents struggling to register for a 30 hours place - with 14 per cent spending more than five hours per week supporting parents. A third of nurseries had problems themselves registering as providers.
"It is important that HMRC gets this right and rolls it out in a way that works for everyone."
The tax-free childcare scheme was first announced in 2013 as an alternative to employer childcare vouchers. Unlike employer childcare vouchers, tax-free childcare is available to the self-employed and targets support with childcare bills on per child rather than per parent basis.
The scheme covers up to £2,000 per child per year and is open to parents who each earn at least £120 a week and no more than £100,000 a year.
More than 275,000 parents have opened an account on the childcare service website, known as Childcare Choices, and also allows families to access the 30 hours free childcare entitlement.