Viral infections impose major stress on the host cell. In response, stress pathways can rapidly deploy defence mechanisms by shutting off the protein synthesis machinery and triggering the accumulation of mRNAs into stress granules to limit the use of energy and nutrients. Because this threatens viral gene expression, viruses need to evade these pathways to propagate. Human norovirus is responsible for gastroenteritis outbreaks worldwide. Here we examined how norovirus interacts with the eIF2α signaling axis controlling translation and stress granules. While norovirus infection represses host cell translation, our mechanistic analyses revealed that eIF2α signaling mediated by the stress kinase GCN2 is uncoupled from translational stalling. Moreover, infection results in a redistribution of the RNA-binding protein G3BP1 to replication complexes and remodelling of its interacting partners, allowing the avoidance from canonical stress granules. These results define novel strategies by which norovirus undergo efficient replication whilst avoiding the host stress response and manipulating the G3BP1 interactome.