In order to clarify the influence of curing temperature on the dynamic properties of steam-cured concrete, series of SHPB tests were conducted to investigate the impact mechanical characteristics of a typical steam-cured concrete applied in prefabricated components of high-speed railway in China. The index of fineness modulus was proposed to evaluate the degree of concrete breakage under different strain rates. The results showed that the peak stress of steam cured concrete increased with increasing the strain rate, while the peak strain showed a decreasing trend, the fineness modulus of broken concrete particles decreased, and the degree of fracture increased obviously. As curing temperature increases, the peak stress of steam-cured concrete decreased significantly, and the concrete specimens showed a stronger strain rate sensitivity. A statistical damage constitutive model considering the strain rate was established and agreed well with the experimental stress–strain curves. Higher temperatures lead to an increase in internal defects of concrete, which makes the impact mechanical properties different from that of normal temperature cured concrete.