In the absence of the scanning ribosomes that unwind mRNA coding sequences and 5′UTRs, mRNAs are likely to form secondary structures and intermolecular bridges. Intermolecular base pairing of non polysomal mRNAs is involved in stress granule (SG) assembly when the pool of mRNAs freed from ribosomes increases during cellular stress. Here, we unravel the structural mechanisms by which a major partner of dormant mRNAs, YB-1 (YBX1), unwinds mRNA secondary structures without ATP consumption by using its conserved cold-shock domain to destabilize RNA stem/loops and its unstructured C-terminal domain to secure RNA unwinding. At endogenous levels, YB-1 facilitates SG disassembly during arsenite stress recovery. In addition, overexpression of wild-type YB-1 and to a lesser extent unwinding-defective mutants inhibit SG assembly in HeLa cells. Through its mRNA-unwinding activity, YB-1 may thus inhibit SG assembly in cancer cells and package dormant mRNA in an unfolded state, thus preparing mRNAs for translation initiation.