This study investigated the dynamic splitting and tensile properties of the precast concrete core samples under different strain rates using the split-Hopkinson pressure bar (SHPB). The dynamic splitting-tensile strength (DSTS), stress-strain curves, and damage patterns of concrete were analyzed. The modified Weibull statistical model was utilized to analyze the discrete features of DSTS and strain rate effects of the precast concrete samples. Besides, the fractal theory was applied to calculate the fractal dimension of surface cracks on core specimens. The relationships between the fractal dimension, splitting-tensile strength, and strain rate effect were also presented. Consequently, it was found that the stress-strain curves of different strength grades of concrete specimens displayed similar patterns. The DSTS of precast concrete exhibited an apparent impact-strengthening effect. And the modified Weibull model proposed in this paper could accurately predict the distribution of DSTS at different strain rates of precast concrete, which provided a theoretical reference for the strength prediction of precast concrete in practical engineering practices. Furthermore, the fractal dimension could qualitatively characterize the failure evolution trend and extent of splitting-tensile damages, providing a new research direction to investigate crack patterns and dynamic mechanical properties of precast concrete members in future engineering inspection and maintenance.