Tissue flow during morphogenesis is commonly driven by local constriction of cell cortices, which is caused by activation of actomyosin contractility. This can lead to long-range flows due to tissue viscosity. However, in the absence of cell-intrinsic polarized forces or polarity in forces external to the tissue, these flows must be symmetric and centered around the region of contraction. Polarized tissue flows have been previously demonstrated to arise from the coupling of such contractile flows to points of increased friction or adhesion to external structures. However, we show with experiments and modeling that the onset of polarized tissue flow in early Drosophila morphogenesis occurs independent of adhesion and is instead driven by a geometric coupling of apical actomyosin contractility to tissue curvature. Particularly, the onset of polarized flow is driven by a mismatch between the position of apical myosin activation and the position of peak curvature at the posterior pole of the embryo. Our work demonstrates how genetic and geometric information inherited from the mother interact to create polarized flow during embryo morphogenesis.