The discovery of several functional interactions where one or even both partners remain disordered has demonstrated that specific interactions do not necessarily require well-defined intermolecular interfaces. Here we describe a fuzzy protein–RNA complex formed by the intrinsically unfolded protein PYM and RNA. PYM is a cytosolic protein, which has been reported to bind the exon junction complex (EJC). In the process of oskar mRNA localization in Drosophila melanogaster, removal of the first intron and deposition of the EJC are essential, while PYM is required to recycle the EJC components after localization has been accomplished. Here we demonstrate that the first 160 amino acids of PYM (PYM^1–160) are intrinsically disordered. PYM^1–160 binds RNA independently of its nucleotide sequence, forming a fuzzy protein–RNA complex that is incompatible with PYM’s function as an EJC recycling factor. We propose that the role of RNA binding consists in down-regulating PYM activity by blocking the EJC interaction surface of PYM until localization has been accomplished. We suggest that the largely unstructured character of PYM may act to enable binding to a variety of diverse interaction partners, such as multiple RNA sequences and the EJC proteins Y14 and Mago.