The paper has been available on the Department for Education (DfE) website since 26 January.
Around half a million seven-year-olds will take the Key Stage one spelling and grammar tests in May when they are at the end of Year two.
The results are used to measure the progress of pupils.
The mistake was noticed by a teacher in south-east England after one of the pupils appeared to be familiar with the material. The school had been conducting an official trial of the exam.
‘Insult’ to pupils and teachers
Lucy Powell, the shadow education secretary, said “the incompetence of ministers at the Department for Education [was] breathtaking”.
“It is an insult to the pupils and teachers who have been working hard to prepare for them,” she added.
A spokesman for the DfE said it had launched an investigation to understand how the test ended up on the website.
He added: “We ask that if anyone has seen the material, they do not share it further so that the test remains helpful for those teachers who have not yet used it with their pupils.”
The spelling test in question has been removed from the DfE’s website, but other samples are still available.