In the adult mouse hippocampus, new neurons are produced by radial glia‐like (RGL) neural stem cells in the subgranular zone, which extend their apical processes toward the molecular layer, and express the astrocyte marker glial fibrillary acidic protein, but not the astrocyte marker S100β. In rodent models of epilepsy, adult hippocampal neurogenesis was reported to be increased after acute and mild seizures, but to be decreased by chronic and severe epilepsy. In the present study, we investigated how the severity of seizures affects neurogenesis and RGL neural stem cells in acute stages of epilepsy, using an improved mouse pilocarpine model in which pilocarpine‐induced hypothermia was prevented by maintaining body temperature, resulting in a high incidence rate of epileptic seizures and low rate of mortality. In mice that experienced seizures without status epilepticus (SE), the number of proliferating progenitors and immature neurons were significantly increased, whereas no changes were observed in RGL cells. In mice that experienced seizures with SE, the number of proliferating progenitors and immature neurons were unchanged, but the number of RGL cells with an apical process was significantly reduced. Furthermore, the processes of the majority of RGL cells extended inversely toward the hilus, and about half of the aberrant RGL cells expressed S100β. These results suggest that seizures with SE lead to changes in the polarity and properties of RGL neural stem cells, which may direct them toward astrocyte differentiation, resulting in the reduction of neural stem cells producing new granule cells. This also suggests the possibility that cell polarity of RGL stem cells is important for maintaining the stemness of adult neural stem cells.