UK's Schools Minister Nick Gibb said the incident was "clearly regrettable".
Half a million seven-year-olds in England had been due to take the tests next month, as part of their Sats.
National Curriculum assessments are a series of educational assessments, known as Sats, used to assess the attainment of children attending maintained schools in England.
On Thursday, the BBC News website reported that a spelling test from this new additional paper had been available on a Department for Education (DfE) website, for use as practice material, since January.
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Russell Hobby, the leader of the National Association of Head Teachers, said: "We have no way of knowing how extensively it has been used by schools and parents."
Gibb issued a statement saying: "To remove any uncertainty and clarify the situation for schools, I have decided that we will remove the requirement on them to administer the Key Stage 1 grammar, punctuation and spelling test for this year only."
The schools minister also announced there would be a "root and branch inquiry" into the Standards and Testing Agency, an agency of the DfE that sets tests.
Jennifer Coupland, chief executive of the Standards and Testing Agency, said the blunder had been caused by "human error".
She said they were alerted that a sample paper posted online contained the live test words rather than the sample test words and removed the document from the website as soon as they were made away.
The test, known as the SPAG, was being introduced this year for children in Year 2. Teaching unions have criticised the move saying it introduced a technical approach to language for children too early.