The inquiry by the education select committee will look at the impact of SATs testing on primary school pupils, and the wider advantages and disadvantages of testing pupils under the age of 11.
In 2014 the government introduced what it called a "far more rigorous curriculum" in primary schools, in order to "raise the bar in terms of expectations of young people's mastery of literacy and numeracy".
Reception baseline assessments were introduced in primary schools in England last year for children as young as four. Although they are not mandatory, the Department for Education encouraged schools to use them, and had planned to use the results to track pupils' progress.
In April the government announced it was ditching plans to use the tests for four as a starting point for measuring pupil progress as they were "not sufficiently comparable", but has indicated that it is looking for an alternative replacement.
Neil Leitch, chief executive of the Pre-school Learning Alliance, said he hopes the inquiry will prompt the government to rethink its approach to primary assessment.
"Over recent years, primary education policy in England has become increasingly focused on testing as a way of measuring and ranking schools, with too little regard to whether it actually benefits children's learning and development.
"Although plans to introduce a reception baseline assessment have been scrapped, the government has been clear that it is still looking for an alternative replacement, and so it's vital that there is clarity on what the purpose of this would be and what it would look like in practice at the earliest possible stage.
Neil Carmichael, chair of the education committee, said: "As a committee we will want to examine how children are assessed, how well the SATs are being delivered, and what steps the government should take in the future to make sure our education system delivers for all children."
The deadline for written submissions is 28 October.