During cytokinesis, a specialized set of proteins is recruited to the equatorial region between spindle poles by microtubules and actin filaments, enabling furrow assembly and ingression before cell division. We investigate the mechanisms underlying regional specialization of the cytoskeleton in HeLa cells undergoing drug-synchronized monopolar cytokinesis. After forced mitotic exit, the cytoskeleton of monopolar mitotic cells is initially radially symmetric but undergoes a symmetry-breaking reaction that simultaneously polarizes microtubules and the cell cortex, with a concentration of cortical furrow markers into a cap at one side of the cell. Polarization requires microtubules, F-actin, RhoA, Myosin II activity, and Aurora B kinase activity. Aurora B localizes to actin cables in a gap between the monopolar midzone and the furrow-like cortex, suggesting a communication between them. We propose that feedback loops between cortical furrow components and microtubules promote symmetry breaking during monopolar cytokinesis and regional specialization of the cytoskeleton during normal bipolar cytokinesis.