Cell constriction promotes epithelial sheet invagination during embryogenesis across phyla. However, how this cell response is linked to global patterning information during organogenesis remains unclear. To address this issue, we have used the Drosophila eye and studied the formation of the morphogenetic furrow (MF), which is characterized by cells undergoing a synchronous apical constriction and apicobasal contraction. We show that this cell response relies on microtubules and F-actin enrichment within the apical domain of the constricting cell as well as on the activation of nonmuscle myosin. In the MF, Hedgehog (Hh) signaling is required to promote cell constriction downstream of cubitus interruptus (ci), and, in this context, Ci155 functions redundantly with mad, the main effector of dpp/BMP signaling. Furthermore, ectopically activating Hh signaling in fly epithelia reveals a direct relationship between the duration of exposure to this signaling pathway, the accumulation of activated Myosin II, and the degree of tissue invagination.