RNA-binding proteins (RBPs) are a major class of proteins that interact with RNAs to change their fate or function. RBPs and the ribonucleoprotein complexes they constitute are involved in many essential cellular processes. In many cases, the molecular details of RBP:RNA interactions differ between viruses, prokaryotes and eukaryotes, making prokaryotic and viral RBPs good potential drug targets. However, targeting RBPs with small molecules has so far been met with limited success as RNA-binding sites tend to be extended, shallow and dynamic with a mixture of charged, polar and hydrophobic interactions. Here, we show that peptide nucleic acids (PNAs) with nucleic acid-like binding properties and a highly stable peptide-like backbone can be used to target some RBPs. We have designed PNAs to mimic the short RNA stem-loop sequence required for the initiation of prokaryotic signal recognition particle (SRP) assembly, a target for antibiotics development. Using a range of biophysical and biochemical assays, the designed PNAs were demonstrated to fold into a hairpin structure, bind the targeted protein and compete with the native RNA hairpin to inhibit SRP formation. To show the applicability of PNAs against other RBPs, a PNA was also shown to bind Nsp9 from SARS-CoV-2, a protein that exhibits non-sequence-specific RNA binding but preferentially binds hairpin structures. Taken together, our results support that PNAs can be a promising class of compounds for targeting RNA-binding activities in RBPs.