Microbial organisms react to their environment and are able to change it through biological and physical processes. For example, fungi exhibit various growth morphologies depending on their host material. Here, we show how the rheological properties of the host material influence the fungal wrinkling morphology. Rheological data of the host material was set in relation to the growth morphology. On host material with high storage modulus, the fungal film was flat, whereas on host material with low storage modulus, the fungus showed a morphology made of folds and wrinkles. We combined our findings with mechanical instability theories and found that the formation of wrinkles and folds is dependent on the storage modulus of the host material. The connection between the wrinkling morphology and the storage modulus of the host material is shown with simple scaling theories. The amplitude, number of wrinkles, and wrinkle length follow geometrical laws, and the mechanical properties of the fungal film are expected to increase with increasing host material elasticity. The obtained results show the connection between living biological films, how they react to their surroundings, and the underlying physical mechanisms. They can provide a framework to further design fungal materials with specific surface morphologies.