After the first furrowing step of animal cell division, the nascent sibling cells remain connected by a thin intercellular bridge (ICB). In isolated cells nascent siblings migrate away from each other to generate tension and constrict the ICB, but less is known about how cells complete cytokinesis when constrained within tissues. We examined the ICBs formed by larval brain neural stem cell (NSC) asymmetric divisions and find that they rely on constriction focused at the central midbody region rather than the flanking arms of isolated cell ICBs. Super-resolution, full volume imaging revealed unexpected oscillatory waves in plasma membrane sheets surrounding the ICB pore during its formation and constriction. We find that these membrane dynamics are driven by Arp2/3-dependent branched actin networks. Inhibition of Arp2/3 complex activity blocks membrane oscillations and prevents ICB formation and constriction. Our results identify a previously unrecognized role for localized membrane oscillations in ICB function when cells cannot generate tension through migration.