The spectacularly curved Banda arc comprises young oceanic crust enclosed by a volcanic inner arc, outer arc islands and a trough parallel to the Australian continental margin. Strong seismic activity in the upper mantle defines a folded surface, for which there are two contrasting explanations: deformation of a single slab or two separate slabs subducting from the north and south. Here we combine seismic tomography with the plate tectonic evolution of the region to infer that the Banda arc results from subduction of a single slab. Our palaeogeographic reconstruction shows that a Jurassic embayment, which consisted of dense oceanic lithosphere enclosed by continental crust, once existed within the Australian plate. Banda subduction began about 15million years ago when active Java subduction tore eastwards into the embayment. The present morphology of the subducting slab is only partially controlled by the shape of the embayment. As the Australian plate moved northward at a high speed of about 7cmyr-1, the Banda oceanic slab rolled back towards the south-southeast accompanied by active delamination separating the crust from the denser mantle. Increasing resistance of the mantle to plate motion progressively folded the slab and caused strong deformation of the crust. The Banda arc represents an outstanding example of large-scale deformation of the Earth's crust in response to coupling between the crust, slab and surrounding mantle.