Functional tissue repair after injury or disease is governed by the regenerative or fibrotic response by cells within the tissue. In the case of corneal damage, keratocytes are a key cell type that determine the outcome of the remodeling response by either adapting to a fibroblast or myofibroblast phenotype. Although a growing body of literature indicates that geometrical cues in the environment can influence Myo(fibroblast) phenotype, there is a lack of knowledge on whether and how differentiated keratocyte phenotype is affected by the curved tissue geometry in the cornea. To address this gap, in this study we characterized the phenotype of fibroblastic and transforming growth factor β (TGFβ)-induced myofibroblastic keratocytes and studied their migration behavior on curved culture substrates with varying curvatures. Immunofluorescence staining and quantification of cell morphological parameters showed that, generally, fibroblastic keratocytes were more likely to elongate, whereas myofibroblastic keratocytes expressed more pronounced α smooth muscle actin (α-SMA) and actin stress fibers as well as more mature focal adhesions. Interestingly, keratocyte adhesion on convex structures was weak and unstable, whereas they adhered normally on flat and concave structures. On concave cylinders, fibroblastic keratocytes migrated faster and with higher persistence along the longitudinal direction compared to myofibroblastic keratocytes. Moreover, this behavior became more pronounced on smaller cylinders (i.e., higher curvatures). Taken together, both keratocyte phenotypes can sense and respond to the sign and magnitude of substrate curvatures, however, myofibroblastic keratocytes exhibit weaker curvature sensing and slower migration on curved substrates compared to fibroblastic keratocytes. These findings provide fundamental insights into keratocyte phenotype after injury, but also exemplify the potential of tuning the physical cell environments in tissue engineering settings to steer towards a favorable regeneration response.