Tissue engineering needs innovative solutions to better fit the requirements of a minimally invasive approach, providing at the same time instructive cues to cells. The use of shape memory polyurethane has been investigated by producing 4D scaffolds via additive manufacturing technology. Scaffolds with two different pore network configurations (0/90° and 0/45°) were characterized by dynamic-mechanical analysis. The thermo-mechanical analysis showed a Tg at about 32 °C (Tg = T trans), indicating no influence of the fabrication process on the transition temperature. In addition, shape recovery tests showed a good recovery of the permanent shape for both scaffold configurations. When cells were seeded onto the scaffolds in the temporary shape and the permanent shape was recovered, cells were significantly more elongated after shape recovery. Thus, the mechanical stimulus imparted by shape recovery is able to influence the shape of cells and nuclei. The obtained results indicate that a single mechanical stimulus is sufficient to initiate changes in the morphology of adherent cells.