Shaping a developing organ or embryo relies on the spatial regulation of cell division and shape. However, morphogenesis also occurs through changes in cell-neighbourhood relationships produced by intercalation. Intercalation poses a special problem in epithelia because of the adherens junctions, which maintain the integrity of the tissue. Here we address the mechanism by which an ordered process of cell intercalation directs polarized epithelial morphogenesis during germ-band elongation, the developmental elongation of the Drosophila embryo. Intercalation progresses because junctions are spatially reorganized in the plane of the epithelium following an ordered pattern of disassembly and reassembly. The planar remodelling of junctions is not driven by external forces at the tissue boundaries but depends on local forces at cell boundaries. Myosin II is specifically enriched in disassembling junctions, and its planar polarized localization and activity are required for planar junction remodelling and cell intercalation. This simple cellular mechanism provides a general model for polarized morphogenesis in epithelial organs.