Thousands of mums and dads are supporting the Let Our Kids Be Kids campaign which is backing a boycott of the Sats tests taken by six and seven-year-olds in Year 2.
Campaigners claim youngsters are being "over-tested, over-worked and in a school system that places more importance on test results and league tables than children's happiness and joy of learning".
The petition adds: "We want our kids to be kids again and enjoy learning for learning's sake, not for Ofsted results or league table figures."
Speaking earlier on Premier Christian Radio's News Hour programme, Clive Ireson, director of the Association of Christian Teachers, said: "Although I have a lot of sympathy for what the parents are saying - 40 thousand of them have signed up to this - I would never condone keeping children out of school. There are better ways to do it.
"The problem with keeping them out of school today is that [Sats] are used for predictions right up to GCSE level. Some schools will be affected by this because the viability of a school is measured by how children do in these tests.
"Teachers in the classroom know how the children are doing. They don't actually need these tests. Teachers assess children anyway and they know those ones that need more help."
You can listen to Clive Ireson speaking with Premier's Antony Bushfield by clicking below.
The move by some parents to keep their children at home today is being branded by the government's Education Secretary, Nicky Morgan, as "harmful".
All pupils should be in school today. Keeping children away will heighten anxiety and prevent us identifying those needing extra help.
— Nick Gibb (@NickGibbMP) 3 May 2016
Schools minister Nick Gibb added: "These tests are vital in helping schools to ensure that young children are learning to read, write and add up well.
"The truth is, if they don't master literacy and numeracy early on, they risk being held behind and struggling for the rest of their lives."
Shadow education secretary Lucy Powell said she did not condone withdrawing children from school but claimed the government had not properly dealt with concerns about Sats.
She added: "This Government is creating chaos and confusion in primary assessment in schools, with a huge number of changes to Sats specifications since children started school last September.