A series of novel Si–O–Si crosslinked organic/inorganic hybrid semi-crystalline polymers with shape memory properties was prepared from alkoxysilane-terminated poly(butylene succinate) (PBS) by water-induced silane crosslinking under organic solvent-free and catalyst-free conditions. The hydrolyzation and condensation of alkoxysilane end groups allowed for the generation of silica-like crosslinking points between the polymeric chains, acting not only as chemical net-points, but also as inorganic filler for a reinforcement effect. The resulting networks were characterized using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), dynamic-mechanical analysis (DMA) and tensile and shape memory tests to gain insight into the relationship between the polymeric structure, the morphology and the properties. By controlling the molecular weight of the PBS precursor, a fine tuning of the crosslinking density and the inorganic content of the resulting network was possible, leading to different thermal, mechanical and shape memory properties. Thanks to their suitable morphology consisting of crystalline domains, which represent the molecular switches between the temporary and permanent shapes, and chemical net-points, which permit the shape recovery, the synthesized materials showed good shape memory characteristics, being able to fix a significant portion of the applied strain in a temporary shape and to restore their original shape above their melting temperature.