We investigate how braneworld gravity affects gravitational collapse and black hole formation by studying Oppenheimer-Snyder-like collapse on a Randall-Sundrum-type brane. Without making any assumptions about the bulk, we prove a no-go theorem: the exterior spacetime on the brane cannot be static, which is in stark contrast with general relativity. We also consider the role of Kaluza-Klein energy density in collapse, using a toy model.