The report by the Welsh Affairs Committee says that the scheme is seen by many as the "imposition on Wales of a solution designed to meet the significantly lower levels of provision in England".
In Wales, 92 per cent of four-year-olds already are in schools, and 51 per cent of three-year-olds are in nursery classes in primary schools. In England, 77 per cent of four-year-olds attend schools for at least part of the year, but in some authorities the percentage is as low as 25 per cent.
Alex Carlile, leader of the Welsh Liberal Democrats, said: "Four-year-olds are critical to many small village schools. The local authority does not have to pay for them, but all do and by doing so cross-subsidise the rest of the school."
The report said: "The Welsh Office itself recognised that in the case of very small schools, even a reduction of a few pupils - for example caused by a family moving out of a village - can have serious implications for the schools' budgets." The loss of two or three four-year-olds to a private nursery could push a school over the margin.
The Welsh local authorities are also concerned because the value of the voucher does not meet the cost of providing high quality education. At Pounds 1,100, it is significantly less than spent by local education authorities in Wales on four-year-olds, which averages at Pounds 1,800.
The report said: "It is argued that the voucher scheme is laying local authorities open to competition without giving them the extra resources they need to compete. Furthermore, they complain they are constrained from raising their own money to meet the costs of new nursery provision by rate-capping. "
It notes that the minister's view is that education authorities are "whingeing because they will be put to administrative inconvenience and will be required for the first time to face up to competition".
The Mudiad Ysgolion Meithrin, the Welsh-medium association for nurseries and playgroups, is concerned many of its groups will not be able to meet the standards, for example of accommodation, required for participation in the scheme.