Cognitive dysfunction constitutes a core characteristic of schizophrenia spectrum disorders (SZ). Specifically, deficits in updating generative models (i.e., cognitive flexibility) and ignoring distracters (i.e., cognitive stability) are considered critical contributors to cognitive impairment in these patients. Here, we examined the structural integrity of frontostriatal networks and their associations with reduced cognitive stability and flexibility in SZ patients. In a sample of 21 patients diagnosed with SZ and 22 healthy controls, we measured grey matter volume (GMV) using structural MRI. Further, cognitive stability and flexibility were assessed using a switch-drift paradigm, quantifying the successful ignoring of distracters and detection of rule switches. Compared to controls, patients showed significantly smaller GMV in the whole brain and three predefined regions of interest: the medial prefrontal cortex (mPFC), inferior frontal gyrus (IFG), and caudate nucleus (CN). Notably, GMV in these areas positively correlated with correct rule-switch detection but not with ignoring rule-compatible drifts. Further, the volumetric differences between SZ patients and controls were statistically explainable by considering the behavioral performance in the switch-drift task. Our results indicate that morphological abnormalities in frontostriatal networks are associated with deficient flexibility in SZ patients and highlight the necessity of minimizing neurodevelopmental and progressive brain atrophy in this population.