The policy is now not likely to become operational for at least a year after the Education Committee decided not to publish a report into the revised plans.
The scheme, which would mean a single point of contact assigned to monitor the wellbeing of every child in Scotland, was ruled unlawful by the UK’s Supreme Court in July last year.
Judges said that while its aim was “legitimate and benign”, its data-sharing aspect was incompatible with the right to privacy under the European Convention on Human Rights.
The SNP has drawn up a new Bill to satisfy the court’s concerns, but the committee insisted that a draft code of practice must be published before they can produce a report.
MSPs have never voted on a bill at stage one without a committee report backing the general principles of the legislation, so the MSPs’ decision will cause a significant delay.
The committee’s stance ignited a row with Education Secretary John Swinney, who has said a code of practice for the Named Person Scheme could not be produced until September next year “at the earliest”.
Some members argued that without one, it was impossible for teachers and others responsible for the scheme to know what their legal responsibilities might be.
“This is a very unusual step for any committee to take, but it is the right one,” Conservative education spokeswoman Liz Smith said.
“Frankly, this whole parliamentary process is a mess and the responsibility for that lies solely with the Scottish Government.
“It is little wonder that so many members of the public are telling John Swinney to cut his losses, ditch the Bill and start again.”
Her Labour counterpart Iain Gray added: “John Swinney’s cack-handed incompetence has created a situation where his own policy is falling apart.
“Rather than trying to force this faulty legislation through without addressing the concerns of parents, practitioners or the courts, Mr Swinney should take responsibility and sort out this mess.”
Last month, The Scotsman revealed the Scottish Government had spent almost £500,000 of taxpayers’ money on legal costs relating to the Named Person Scheme.
Campaigners against the policy believe it represents “unjustifiable state interference with family rights” and will stretch existing resources by including children who do not need help.
But children’s charities have backed the plans, arguing they will merely give young people and parents a single point of contact if they need extra support.
A Scottish Government spokesman said: “We are disappointed by the Committee’s decision to unnecessarily seek to delay progress of this important Bill.
“As [Mr Swinney] has already clearly set out, the new code of practice will be subject to Parliamentary scrutiny and approval, while an independent panel will ensure the code and other support material is workable.”