Plans to introduce a baseline assessment for Reception pupils are being delayed a year to September 2021.
The Department for Education has written to all primary schools in England following discussions with head teachers' unions.
Heads had been pushing for a delay to the introduction of the assessment designed to check where pupils are when they enter school.
The assessment is part of a system of tests to track pupils' progress.
School standards minister, Nick Gibb, said: "As we prepare for all children to return to school in September, I know teachers are working tirelessly to provide extra support to children to recover from the impact of the coronavirus.
"In light of these circumstances, we have decided to postpone the statutory rollout of the Reception Baseline Assessment until September 2021."
The new baseline assessment will be used to assess pupils' maths, language and literacy skills when they enter primary and, ultimately, to hold schools to account for pupil progress.
National Association of Head Teachers general secretary Paul Whiteman said: "There is no certainty in the current time as to what will happen in the autumn term and there is potential of further disruption to the 2020-2021 academic year.
"Furthermore we know there will be plenty of recovery work to do and that most children will not take part in the usual transition activities prior to starting school.
"Schools will rightly need to be focussing on this vital work as they return in the new academic year."
Children in England face statutory tests at the age of seven which are due to be scrapped in three years time - however, Mr Whiteman said he feared this date might also be delayed.
Geoff Barton of the Association of School and College Leaders said the decision was a "pragmatic and sensible" one.
He added that this was not the time to introduce a new national assessment.
"However, the government must also undertake a review of Key Stage 2 tests due to be taken next May as a matter of urgency."
Mr Barton said the Key Stage 2 tests, which are taken by 11-year-olds, should not be used as the basis of primary school league tables "after so much disruption".