RNA G-quadruplexes (RG4s) are four-stranded structures known to control mRNA translation of cancer relevant genes. RG4 formation is pervasive in vitro but not in cellulo, indicating the existence of a poorly characterized molecular machinery that remodels RG4s and maintains them unfolded. To help fill this gap in knowledge, we performed a quantitative proteomic screen to identify cytosolic proteins that interact with a canonical RG4 in its folded and unfolded conformation. Our results identified hnRNP H/F as important components of the cytoplasmic machinery modulating RG4s structural integrity, revealed their function in RG4-mediated translation and uncovered the underlying molecular mechanism impacting cellular stress response linked to the outcome of glioblastoma, one of the deadliest types of solid cancer overall.