Neural stem cells (NSCs) are multipotent and correct fate determination is crucial to guarantee brain formation and homeostasis. How NSCs are instructed to generate neuronal or glial progeny is not well understood. Here, we addressed how murine adult hippocampal NSC fate is regulated and described how scaffold attachment factor B (SAFB) blocks oligodendrocyte production to enable neuron generation. We found that SAFB prevents NSC expression of the transcription factor nuclear factor I/B (NFIB) by binding to sequences in the Nfib mRNA and enhancing Drosha-dependent cleavage of the transcripts. We show that increasing SAFB expression prevents oligodendrocyte production by multipotent adult NSCs, and conditional deletion of Safb increases NFIB expression and oligodendrocyte formation in the adult hippocampus. Our results provide novel insights into a mechanism that controls Drosha functions for selective regulation of NSC fate by modulating the post-transcriptional destabilization of Nfib mRNA in a lineage-specific manner.