Different from animal cells that divide by constriction of the cortex inward, cells of land plants divide by initiating a new cell-wall segment from their center. For this, a disk-shaped, membrane-enclosed precursor termed the cell plate is formed that radially expands toward the parental cell wall [1-3]. The synthesis of the plate starts with the fusion of vesicles into a tubulo-vesicular network [4-6]. Vesicles are putatively delivered to the division plane by transport along microtubules of the bipolar phragmoplast network that guides plate assembly [7-9]. How vesicle immobilization and fusion are then locally triggered is unclear. In general, a framework for how the cytoskeleton spatially defines cell-plate formation is lacking. Here we show that membranous material for cell-plate formation initially accumulates along regions of microtubule overlap in the phragmoplast of the moss Physcomitrella patens. Kinesin-4-mediated shortening of these overlaps at the onset of cytokinesis proved to be required to spatially confine membrane accumulation. Without shortening, the wider cell-plate membrane depositions evolved into cell walls that were thick and irregularly shaped. Phragmoplast assembly thus provides a regular lattice of short overlaps on which a new cell-wall segment can be scaffolded. Since similar patterns of overlaps form in central spindles of animal cells, involving the activity of orthologous proteins [10, 11], we anticipate that our results will help uncover universal features underlying membrane-cytoskeleton coordination during cytokinesis.