N6-methyladenosine (m6A) is deposited co-transcriptionally on thousands of cellular mRNAs and plays important roles in mRNA processing and cellular function. m6A is particularly abundant within the brain and is critical for neurodevelopment. However, the mechanisms through which m6A contributes to brain development are incompletely understood. RBM45 acts as an m6A-binding protein that is highly expressed during neurodevelopment. We find that RBM45 binds to thousands of cellular RNAs, predominantly within intronic regions. Rbm45 depletion disrupts the constitutive splicing of a subset of target pre-mRNAs, leading to altered mRNA and protein levels through both m6A-dependent and m6A-independent mechanisms. Finally, we find that RBM45 is necessary for neuroblastoma cell differentiation and that its depletion impacts the expression of genes involved in several neurodevelopmental signaling pathways. Altogether, our findings show a role for RBM45 in controlling mRNA processing and neuronal differentiation, mediated in part by the recognition of methylated RNA.