The TRAnsport Protein Particle (TRAPP) complex controls multiple membrane trafficking steps and is strategically positioned to mediate cell adaptation to diverse environmental conditions, including acute stress. We have identified the TRAPP complex as a component of a branch of the integrated stress response that impinges on the early secretory pathway. The TRAPP complex associates with and drives the recruitment of the COPII coat to stress granules (SGs) leading to vesiculation of the Golgi complex and arrest of ER export. The relocation of the TRAPP complex and COPII to SGs only occurs in cycling cells and is CDK1/2‐dependent, being driven by the interaction of TRAPP with hnRNPK, a CDK substrate that associates with SGs when phosphorylated. In addition, CDK1/2 inhibition impairs TRAPP complex/COPII relocation to SGs while stabilizing them at ER exit sites. Importantly, the TRAPP complex controls the maturation of SGs. SGs that assemble in TRAPP‐depleted cells are smaller and are no longer able to recruit RACK1 and Raptor, two TRAPP‐interactive signaling proteins, sensitizing cells to stress‐induced apoptosis.