The Year 6 pupils from Dog Kennel Hill Primary in East Dulwich, south London, have called for the minister to follow the example of Wales and scrap the exams.
Two pupils described how Sats and test preparation, had made them cry, while several said testing had made them ill with worry.
Earlier this term, the pupils asked Katherine Nicholls, their teacher, how to protest against the tests. She suggested writing to Mr Knight, then played them parts of a Panorama television documentary on over-testing, in which he appeared last month.
In the programme, Mr Knight played down concerns about teaching to the test, claiming that it "need not be a huge deal" and that "children don't notice hugely that they're taking national tests as opposed to other tests."
Miss Nicholls said she was incensed by his comments and felt they were an insult to her and her colleagues, who frequently felt pressurised to improve test results.
Her school had a good Ofsted report and its teachers keep test preparation to one month before the tests. But Miss Nicholls said she found it increasingly difficult to hide this pressure from pupils.
In her letter to Mr Knight, she said: "I would challenge you to find any English primary school where the children are not aware that they are taking 'important' national tests.
"I am tired of the Government's fundamentally flawed use of Sats results as a measure of school success, and I am devastated that I have had to watch another class go through the emotional trauma."
Several of the 27 children who wrote to the minister said they missed out on lessons such as art, PE, history and geography.
Most also wrote of feeling relieved once they were over. Some describe the tests themselves as a trial, although a handful said they were easier than expected.
They accompanied their letters with drawings showing how they imagined Sats, depicting them as fierce monsters (see panel, right).
Miss Nicholls wrote that she had noticed that pupils' behaviour worsened as the tests drew near.
National tests have come under sustained criticism from academics and teachers' unions.