Eukaryotic cell division requires dependency relationships in which late processes commence only after early ones are appropriately completed. We have discovered a system that blocks late events of cytokinesis until early ones are successfully accomplished. In budding yeast, cytokinetic actomyosin ring contraction and membrane ingression are coupled with deposition of an extracellular septum that is selectively degraded in its primary septum immediately after its completion by secreted enzymes. We find this secretion event is linked to septum completion and forestalled when the process is slowed. Delay of septum degradation requires Fir1, an intrinsically disordered protein localized to the cytokinesis site that is degraded upon septum completion but stabilized when septation is aberrant. Fir1 protects cytokinesis in part by inhibiting a separation-specific exocytosis function of the NDR/LATS kinase Cbk1, a key component of “hippo” signaling that induces mother–daughter separation. We term this system enforcement of cytokinesis order, a checkpoint ensuring proper temporal sequence of mechanistically incompatible processes of cytokinesis.