Peroxisomes are ubiquitous organelles whose dysfunction causes fatal human diseases. Most peroxisomal proteins are imported from the cytosol in a folded state by the soluble receptor PEX5. How folded cargo crosses the membrane is unknown. Here, we show that peroxisomal import is similar to nuclear transport. The peroxisomal membrane protein PEX13 contains a conserved tyrosine (Y)– and glycine (G)–rich YG domain, which forms a selective phase resembling that formed by phenylalanine-glycine (FG) repeats within nuclear pores. PEX13 resides in the membrane in two orientations that oligomerize and suspend the YG meshwork within the lipid bilayer. Purified YG domains form hydrogels into which PEX5 selectively partitions, by using conserved aromatic amino acid motifs, bringing cargo along. The YG meshwork thus forms an aqueous conduit through which PEX5 delivers folded proteins into peroxisomes.