Cytokinesis is the process where the mother cell's cytoplasm separates into daughter cells. This is driven by an actomyosin contractile ring that produces cortical contractility and drives cleavage furrow ingression, resulting in the formation of a thin intercellular bridge. While cytoskeletal reorganization during cytokinesis has been extensively studied, less is known about the spatiotemporal dynamics of the plasma membrane. Here, we image and model plasma membrane lipid and protein dynamics on the cell surface during leukemia cell cytokinesis. We reveal an extensive accumulation and folding of the plasma membrane at the cleavage furrow and the intercellular bridge, accompanied by a depletion and unfolding of the plasma membrane at the cell poles. These membrane dynamics are caused by two actomyosin-driven biophysical mechanisms: the radial constriction of the cleavage furrow causes local compression of the apparent cell surface area and accumulation of the plasma membrane at the furrow, while actomyosin cortical flows drag the plasma membrane toward the cell division plane as the furrow ingresses. The magnitude of these effects depends on the plasma membrane fluidity, cortex adhesion, and cortical contractility. Overall, our work reveals cell-intrinsic mechanical regulation of plasma membrane accumulation at the cleavage furrow that is likely to generate localized differences in membrane tension across the cytokinetic cell. This may locally alter endocytosis, exocytosis, and mechanotransduction, while also serving as a self-protecting mechanism against cytokinesis failures that arise from high membrane tension at the intercellular bridge.