While the effects of anxiety on various cognitive processes, including memory, attention, and learning, have been relatively well documented, the neurobiological effects of anxiety on social cognitive processes remain largely unknown. We address this gap using threat-of-shock to induce incidental anxiety while participants performed two false-belief tasks, a standard and an economic-games version. During belief formation and belief inferences, regions in a canonical social cognition network showed activation reflecting mentalizing, including the temporoparietal junction (TPJ), precuneus, and dorsomedial prefrontal cortex (dmPFC). At the same time, we found threat-related suppression of social cognition regions during belief inferences. A conjunction analysis confirmed that a network of regions was simultaneously engaged during mentalizing and suppressed by anxiety: bilateral TPJ, bilateral IFG, and putamen. We examined how threat impacted the connectivity between seed regions from the conjunction analyses and its targets. During belief formation, we found that anxiety suppressed the connectivity between the precuneus seed and two key mentalizing nodes, the dmPFC and right TPJ. Moreover, during belief inferences threat specificallty suppressed belief-based connectivity between putamen and its targets in IPS and dlPFC, and dispositional distress significantly modulated threat-related suppression of connectivity between the left TPJ seed and left IPS. Our results highlight important effects of incidental and dispositional anxiety on specific nodes of the social cognition network. Taken together, our study uncovers novel interactions between the reward, social cognition, and attentional systems, indicating that social cognitive processes rely on support from other large-scale networks, and that these network interactions are disrupted under incidental anxiety.