Post-transcriptional mechanisms regulate the stability and, hence, expression of coding and noncoding RNAs. Sequence-specific features within the 3' untranslated region (3' UTR) often direct mRNAs for decay. Here, we characterize a genome-wide RNA decay pathway that reduces the half-lives of mRNAs based on overall 3' UTR structure formed by base pairing. The decay pathway is independent of specific single-stranded sequences, as regulation is maintained in both the original and reverse complement orientation. Regulation can be compromised by reducing the overall structure by fusing the 3' UTR with an unstructured sequence. Mutating base-paired RNA regions can also compromise this structure-mediated regulation, which can be restored by re-introducing base-paired structures of different sequences. The decay pathway requires the RNA-binding protein UPF1 and its associated protein G3BP1. Depletion of either protein increased steady-state levels of mRNAs with highly structured 3' UTRs as well as highly structured circular RNAs. This structure-dependent mechanism therefore enables cells to selectively regulate coding and noncoding RNAs.