Spliceosomal snRNPs are multicomponent particles that undergo a complex maturation pathway. Human Sm-class snRNAs are generated as 3′-end extended precursors, which are exported to the cytoplasm and assembled together with Sm proteins into core RNPs by the SMN complex. Here, we provide evidence that these pre-snRNA substrates contain compact, evolutionarily conserved secondary structures that overlap with the Sm binding site. These structural motifs in pre-snRNAs are predicted to interfere with Sm core assembly. We model structural rearrangements that lead to an open pre-snRNA conformation compatible with Sm protein interaction. The predicted rearrangement pathway is conserved in Metazoa and requires an external factor that initiates snRNA remodeling. We show that the essential helicase Gemin3, which is a component of the SMN complex, is crucial for snRNA structural rearrangements during snRNP maturation. The SMN complex thus facilitates ATP-driven structural changes in snRNAs that expose the Sm site and enable Sm protein binding.