This paper aimed to analyze fundamental movement skill (FMS) assessment tools that could be used for primary school children. In this narrative review, the Motoriktest für Vier- bis Sechjärige Kinder (MOT 4–6), Movement Assessment Battery for Children-2 (M-ABC-2), Motorische Basiskompetenzen (MOBAK) Körperkoordinationtest für Kinder (KTK), Test of Gross Motor Development (TGMD), Maastricht Motoriek Test (MMT) and the Bruininks–Oseretsky Test of Motor Proficiency-2 (BOT-2) were analyzed from a methodological perspective, such as the number of test items, tools and types of tests, in terms of the FMS area. The analysis revealed that to assess locomotor movement skills, the BOT-2 has an excellent test for running ability, but for detecting technical difficulties, the TGMD is recommended. To test hopping, the MMT is the best test. Object control movement skills are measured with throws, dribbles and catches. Most of the tools assessed these skills, but it turned out that the TGMD is the best for measuring object control. Stability movement skills are tested with static and dynamic balance tests. Dynamic balance is more frequently used, and the MOT 4–6, KTK and BOT-2 have the most tools to use. However, the MMT is an excellent test for static balance. Fine motor movement skills are easy to assess with the MMT and MOT 4–6, since they have low equipment requirements. The BOT-2 is the best measurement tool; however, it has high equipment requirements. All of the FMS assessment tools are good; however, we concluded that although these tools are excellent for research purposes, they are difficult to apply in a school setting. Thus, teachers and coaches are advised to always select a single task from the available assessment tools that is appropriate for the skills they would like to measure.