The present study investigated the relationship between linguistic tone processing and cortical thickness of bilateral planum temporale (PT) and pars opercularis of the inferior frontal gyrus (IFGpo). Swedish tones on word stems function as cues to upcoming endings. Correlating structural brain imaging data with participants’ response time patterns for suffixes, we found that thicker cortex in the left PT was associated with greater reliance on tones to anticipate upcoming inflections on real words. On inflected pseudoword stems, however, the cortical thickness of left IFGpo was associated with tone-suffix processing. Thus cortical thickness of the left PT might play a role in processing tones as part of stored representations for familiar speech segments, most likely when inflected forms are accessed as whole words. In the absence of stored representations, listeners might need to rely on morphosyntactic rules specifying tone-suffix associations, potentially facilitated by greater cortical thickness of left IFGpo.