Some 24,000 children in 267 schools took the NI Numeracy Assessment (NINA) and NI Literacy Assessment (NILA) tests in 2016/17.
However, 17,000 pupils who took last autumn's maths tests initially received lower scores than they achieved.
The Council for the Curriculum, Examinations and Assessment (CCEA) apologised "unreservedly".
The tests are used to assess maths skills and the progress of pupils in P4 to P7.
Paying for them cost CCEA about Â£400,000 per year.
In a letter to schools who used the tests, the Department of Education said the minister had decided that "the existing contracts for NINA and NILA should not be renewed".
The letter, dated 17 January, also said that CCEA would not be asked to develop a replacement for the tests.
"The minister is fully aware of the challenging financial position facing schools this year and looking likely to continue in future years," the letter said.
"He could not justify extending the contract beyond the 2016/17 academic year."
The letter also said the education sector was facing "considerable financial constraints".
Both the computer-based NINA and the NILA tests were the subject of a critical Department of Education review in 2014, following widespread technical problems experienced by pupils taking the tests.
Following that, the then education minister John O'Dowd said the tests were not mandatory for schools.
However, about a third of primary schools still used them to assess the performance and skills of pupils in English and maths.
The Education Minister Peter Weir has ended computer based tests in maths and English for primary school pupils.