Although brain rhythms depend on brain structure (e.g., gray and white matter), to our knowledge associations between brain oscillations and structure have not been investigated in healthy controls (HC) or in individuals with schizophrenia (SZ). Observing function–structure relationships, for example establishing an association between brain oscillations (defined in terms of amplitude or phase) and cortical gray matter, might inform models on the origins of psychosis. Given evidence of functional and structural abnormalities in primary/secondary auditory regions in SZ, the present study examined how superior temporal gyrus (STG) structure relates to auditory STG low-frequency and 40Hz steady-state activity. Given changes in brain activity as a function of age, age-related associations in STG oscillatory activity were also examined.Thirty-nine individuals with SZ and 29 HC were recruited. 40Hz amplitude-modulated tones of 1s duration were presented. MEG and T1-weighted sMRI data were obtained. Using the sources localizing 40Hz evoked steady-state activity (300 to 950ms), left and right STG total power and inter-trial coherence were computed. Time–frequency group differences and associations with STG structure and age were also examined.Decreased total power and inter-trial coherence in SZ were observed in the left STG for initial post-stimulus low-frequency activity (~50 to 200ms, ~4 to 16Hz) as well as 40Hz steady-state activity (~400 to 1000ms). Left STG 40Hz total power and inter-trial coherence were positively associated with left STG cortical thickness in HC, not in SZ. Left STG post-stimulus low-frequency and 40Hz total power were positively associated with age, again only in controls.Left STG low-frequency and steady-state gamma abnormalities distinguish SZ and HC. Disease-associated damage to STG gray matter in schizophrenia may disrupt the age-related left STG gamma-band function–structure relationships observed in controls.