The excellent overall performance of polyoxymethylene (POM) fiber enables it to show great potential for engineering applications. The effect of POM fibers on the dynamic compression mechanical properties of concrete is an important issue for its application in engineering structures such as airport pavement and bridges. It is necessary to investigate the dynamic compressive mechanical properties of POM-fiber-reinforced concrete (PFRC) under impact loading. The PFRC specimens with various POM fiber lengths (6, 8, 12, 16, and 24 mm) and ordinary-performance concrete (OPC) specimens were tested by utilizing the split Hopkinson pressure bar (SHPB). We studied the effect of fiber length and strain rate on the dynamic compression mechanical properties of PFRC and established a damage dynamic constitutive model for PFRC. The results indicate that the dynamic compressive strength, peak strain, ultimate strain, dynamic peak toughness, dynamic ultimate toughness, and dynamic increase factor (DIF) of the PFRC increased obviously with the increase in strain rate. POM fiber was found to be able to effectively improve the deformation ability and impact toughness of concrete. The dynamic compressive strength and impact toughness of PFRC with a fiber length of 8 mm was optimal at different strain rates. The POM fibers with 16 mm and 24 mm lengths negatively affected the dynamic compressive strength of the concrete. The fiber length variation had an insignificant effect on the DIF of PFRC. The established damage dynamic constitutive model for PFRC was fitted and analyzed, and it was found that the model is able to describe the dynamic characteristics of PFRC well. This study can extend POM fibers to engineering structures that may be subjected to impact loading and act as a reference for the design of PFRC under impact loading.