The promyelocytic leukemia (PML) protein organizes PML nuclear bodies (NBs), which are stress-responsive domains where many partner proteins accumulate. Here, we clarify the basis for NB formation and identify stress-induced partner sumoylation as the primary NB function. NB nucleation does not rely primarily on intermolecular interactions between the PML SUMO-interacting motif (SIM) and SUMO, but instead results from oxidation-mediated PML multimerization. Oxidized PML spherical meshes recruit UBC9, which enhances PML sumoylation, allow partner recruitment through SIM interactions, and ultimately enhance partner sumoylation. Intermolecular SUMO-SIM interactions then enforce partner sequestration within the NB inner core. Accordingly, oxidative stress enhances NB formation and global sumoylation in vivo. Some NB-associated sumoylated partners also become polyubiquitinated by RNF4, precipitating their proteasomal degradation. As several partners are protein-modifying enzymes, NBs could act as sensors that facilitate and confer oxidative stress sensitivity not only to sumoylation but also to other post-translational modifications, thereby explaining alterations of stress response upon PML or NB loss.