Mitotic cells assume a spherical shape by increasing their surface tension and osmotic pressure by extensively reorganizing their interphase actin cytoskeleton into a cortical meshwork and their microtubules into the mitotic spindle. Mitotic entry is known to interfere with tissue morphogenetic events that require cell-shape changes controlled by the interphase cytoskeleton, such as apical constriction. However, here we show that mitosis plays an active role in the epithelial invagination of the Drosophila melanogaster tracheal placode. Invagination begins with a slow phase under the control of epidermal growth factor receptor (EGFR) signalling; in this process, the central apically constricted cells, which are surrounded by intercalating cells, form a shallow pit. This slow phase is followed by a fast phase, in which the pit is rapidly depressed, accompanied by mitotic entry, which leads to the internalization of all the cells in the placode. We found that mitotic cell rounding, but not cell division, of the central cells in the placode is required to accelerate invagination, in conjunction with EGFR-induced myosin II contractility in the surrounding cells. We propose that mitotic cell rounding causes the epithelium to buckle under pressure and acts as a switch for morphogenetic transition at the appropriate time.