Interventional radiology technique (IRT) is being increasingly used to embolize the blood vessels or prevent the flow of blood into the diseased part of a blood vessel in a human body. Shape memory polyurethane (SMPU) has been identified as an alternate embolic agent for IRT, which can overcome vital issues such as non-target embolization, incomplete occlusion, coil migration, and others. However, its inherent lack of radiopacity and bioinertness restrict potential applications of it in IRT. The objective of the present work is to study the effect of combining SMPU and radiopaque filler materials on the mechanical, thermal, shape recovery characteristics, and radiopacity. Hybrid composite materials having Barium sulphate (BaSO4) nanoparticles and hydroxyapatite (HaP) nanoparticles in the SMPU matrix are fabricated using a twin-screw extruder, and their properties are compared with that of the composites containing only single filler. The addition of the filler in SMPU is not found to affect its shape-holding characteristics. However, the shape recovery characteristics of the hybrid composites are decreased by 20–30% during the 1st cycle, which was then recovered to more than 90% during the 2nd recovery cycle. It is observed that the shape recovery rate of the SMPU can be fine-tuned by changing its programming temperature. It is also noted that the tensile strength of composites is decreased with an increase of filler concentration due to their agglomeration and voids in the composites. In case of 10 wt% hybrid composites, the reduction of tensile strength is found to be in the range of 24–28% irrespective of individual filler concentration, and it showed better mechanical properties than individual filler at the same concentration. The radiopacity of the composites is observed to be increased with filler concentration, where BaSO4 played a dominant role in comparison to that of hydroxyapatite nanoparticles. Hence, the developed SMPU hybrid nanocomposites can be explored as embolic agents for IRT due to their suitable mechanical properties, actuation profiles, and enhanced radiopacity.