The nuclear envelope (NE) aids in organizing the interphase genome by tethering chromatin to the nuclear periphery. During mitotic entry, NE-chromatin contacts are broken. Here, we report on the consequences of impaired NE removal from chromatin for cell division of human cells. Using a membrane-chromatin tether that cannot be dissociated when cells enter mitosis, we show that a failure in breaking membrane-chromatin interactions impairs mitotic chromatin organization, chromosome segregation and cytokinesis, and induces an aberrant NE morphology in postmitotic cells. In contrast, chromosome segregation and cell division proceed successfully when membrane attachment to chromatin is induced during metaphase, after chromosomes have been singularized and aligned at the metaphase plate. These results indicate that the separation of membranes and chromatin is critical during prometaphase to allow for proper chromosome compaction and segregation. We propose that one cause of these defects is the multivalency of membrane-chromatin interactions.