The cytokinetic cleavage furrow is typically positioned symmetrically relative to the cortical cell boundaries, but it can also be asymmetric. The mechanisms that control furrow site specification have been intensively studied, but how polar cortex movements influence ultimate furrow position remains poorly understood. We measured the position of the apical and the basal cortex in asymmetrically dividing Drosophila neuroblasts and observed preferential displacement of the apical cortex that becomes the larger daughter cell during anaphase, effectively shifting the cleavage furrow toward the smaller daughter cell. Asymmetric cortical extension is correlated with the presence of cortical myosin II, which is polarized in neuroblasts. Loss of myosin II asymmetry by perturbing heterotrimeric G-protein signaling results in symmetric extension and equal-sized daughter cells. We propose a model in which contraction-driven asymmetric polar extension of the neuroblast cortex during anaphase contributes to asymmetric furrow position and daughter cell size.