Morphogenetic epithelial movement occurs during embryogenesis and drives complex tissue formation. However, how epithelial cells coordinate their unidirectional movement while maintaining epithelial integrity is unclear. Here we propose a novel mechanism for collective epithelial cell movement based on Drosophila genitalia rotation, in which epithelial tissue rotates clockwise around the genitalia. We found that this cell movement occurs autonomously and requires myosin II. The moving cells exhibit repeated left–right-biased junction remodelling, while maintaining adhesion with their neighbours, in association with a polarized myosin II distribution. Reducing myosinID, known to cause counter-clockwise epithelial-tissue movement, reverses the myosin II distribution. Numerical simulations revealed that a left–right asymmetry in cell intercalation is sufficient to induce unidirectional cellular movement. The cellular movement direction is also associated with planar cell-shape chirality. These findings support a model in which left–right asymmetric cell intercalation within an epithelial sheet drives collective cellular movement in the same direction.