The low-velocity impact response of sandwich structures with aluminum face sheets and neat or nano-reinforced polypropylene core was studied. A strain-rate dependent micromechanics model (SRDM) was presented in the literature for predicting the dynamic behavior of nano-reinforced polymers. In the present study, the dynamic behavior of nano-reinforced polypropylene was simulated based on SRDM results. The finite element model was validated against the experimental results. It was shown that the results of the simulation performed by the SRDM model were in very good agreement with the experimental data. Then, the proposed finite element model was used for checking the sensitivity of the impact performance of nano-reinforced sandwich structures to the material and geometrical variations. A special sandwich structure with a core of 1 mm thickness and a face thickness of 1 mm was considered as the base structure. Different material and geometrical variations including doubling the thickness of the core or face sheets, a different weight ratio of graphene, and increasing material parameters of the face sheets up to 90%, were undertaken on the base structure. The results of the present study imply that the optimal amount of graphene should not exceed 0.5 wt.% to improve impact properties. The impact response of nano-reinforced sandwich structures was more sensitive to the variations of the face thickness in comparison to the variations of the core thickness. Moreover, the impact outputs were more sensitive to changes in the yield stress of faces compared to changes in Young’s modulus of faces.