Muslim families in receipt of Child Trust Fund vouchers are currently unable to use them as the available accounts do not comply with Sharia law.
No providers have yet committed to offering a suitable account
Islamic law forbids all forms of financial interest and has strict rules about the kind of products Muslims can invest in.
And if the industry does not respond to the demand, in a year the Inland Revenue will invest on behalf of these families, against their religion.
However, the Inland Revenue told the BBC it hopes the finance industry will set up a Sharia compliant account as there is nothing in the rules to prevent it from doing so.
The new Child Trust Fund (CTF) will be launched in April, and all parents of children born from 1 September, 2002, are getting at least £250 from the government to invest in special accounts for their child's future.
There are currently 29 CTF accounts available in the UK, with some allowing parents to save in interest-paying cash accounts, and others which invest in shares.
But as Ibrahim Mogra, a Leicester Muslim explained:
"Unfortunately, at the moment there is no CTF where I could invest that money on behalf of my child because the places where the government has recommended are not Sharia compliant."
Other ethical investors also face a lack of choice. There is only one suitable account, which is being offered by the Co-operative Insurance Society (CIS).
Speaking to Money Box, Natalie Kurpas of the CIS said:
"The funds are not invested in any tobacco companies, any weapons, arms or nuclear power companies, anything like that. It is the only ethical stakeholder CTF."
However, the lack of choice concerns Scott McAusland from EIRIS, the Ethical Investment Research Service. He told Money Box:
"It is important there are more funds that match the principles and views of the investors, of the parents who are investing on behalf of their children, which match the aspirations they have for their children and the sort of world in which their children will grow up."
Investors' money from the CIS Child Trust Fund will be channelled into the CIS FTSE4 Good Tracker Trust with performance linked to the FTSE4Good UK share index.
Jeremy Batstone, director of research for Charles Stanley Stockbrokers, explained:
"It is essentially an index made up of those companies regarded as being ethically or environmentally-friendly.
"It is not the same as the main FTSE 100 index as that comprises of certain companies that under certain criteria might not make ethically or environmentally-friendly portfolios."
But this fund is not suitable for Muslims, as Faysal Sattar of Britain's only firm of Muslim financial advisers, 1st Ethical, explained.
He said the CIS Child Trust Fund and FTSE4GOOD Index are not Sharia compliant because they are not strict enough in the firms they invest in.
However, Mr Sattar is hopeful the situation will change.
He is a member of the Muslim Council of Britain's economic steering committee which advises the government on such matters, and he told the programme:
"We are hoping we can bring this matter up and try to think about a fund that will be able to cater for the Muslim community."