Recent decades have seen substantial interest in the development and application of biocompatible shape memory polymers (SMPs), a class of “smart materials” that can respond to external stimuli. Although many studies have used SMP platforms triggered by thermal or photothermal events to study cell mechanobiology, SMPs triggered by cell activity have not yet been demonstrated. In a previous work, we developed an SMP that can respond directly to enzymatic activity. Here, our goal was to build on that work by demonstrating enzymatic triggering of an SMP in response to the presence of enzyme-secreting human cells. To achieve this phenomenon, poly(ε-caprolactone) (PCL) and Pellethane were dual electrospun to form a fiber mat, where PCL acted as a shape-fixing component that is labile to lipase, an enzyme secreted by multiple cell types including HepG2 (human hepatic cancer) cells, and Pellethane acted as a shape memory component that is enzymatically stable. Cell-responsive shape memory performance and cytocompatibility were quantitatively and qualitatively analyzed by thermal analysis (thermal gravimetric analysis and differential scanning calorimetry), surface morphology analysis (scanning electron microscopy), and by incubation with HepG2 cells in the presence or absence of heparin (an anticoagulant drug present in the human liver that increases the secretion of hepatic lipase). The results characterize the shape-memory functionality of the material and demonstrate successful cell-responsive shape recovery with greater than 90% cell viability. Collectively, the results provide the first demonstration of a cytocompatible SMP responding to a trigger that is cellular in origin.