The cytoskeleton is a major determinant of cell-shape changes that drive the formation of complex tissues during development. Important roles for actomyosin during tissue morphogenesis have been identified, but the role of the microtubule cytoskeleton is less clear. Here, we show that during tubulogenesis of the salivary glands in the fly embryo, the microtubule cytoskeleton undergoes major rearrangements, including a 90° change in alignment relative to the apicobasal axis, loss of centrosomal attachment, and apical stabilization. Disruption of the microtubule cytoskeleton leads to failure of apical constriction in placodal cells fated to invaginate. We show that this failure is due to loss of an apical medial actomyosin network whose pulsatile behavior in wild-type embryos drives the apical constriction of the cells. The medial actomyosin network interacts with the minus ends of acentrosomal microtubule bundles through the cytolinker protein Shot, and disruption of Shot also impairs apical constriction.