For the first time in this paper, a composite sandwich panel with a novel circular-shaped core reinforced with silica nanoparticles (SNPs) is designed and fabricated using the vacuum-assisted resin transfer molding (VARTM) method. Carbon fibers and epoxy resin are utilized to construct the composite sandwich panels, followed by polyurethane foam injection. After fabrication, the sandwich panels undergo uniform compression testing to examine their mechanical behavior and properties. In this study, the effects of various parameters, such as core length, core height, weight percentage (wt.%) of SNPs, and polyurethane foam, on the compressive strength of the structure are evaluated. To validate the results, a finite element simulation of the sandwich panel compression test is performed using ABAQUS software, and the results obtained are compared with experimental data, showing good agreement. The results of this research demonstrate that adding SNPs within a specific range results in a considerable enhancement of the structural strength. Adding SNPs up to 3% leads to approximately a 19% increase in the compressive strength of the structure. However, adding 4 wt.% SNPs results in a decrease of about 12% in the strength of the sandwich panel. Additionally, the core’s geometry significantly influences the control of compressive strength and rigidity of the sandwich panel. In other words, by increasing the core length, the compressive strength increases by 38%, while increasing the core height decreases compressive strength by about 30%. Also, it is found that adding polyurethane foam to the sandwich panel, despite a slight increase in weight, leads to a significant increase in compressive strength by about 32% and postpones its ultimate failure. Eventually, the hybrid specimen exhibits a strength approximately 57% greater than that of the pure foamless sandwich panel.