Free-living animals cope with environmental stressors through physiological and behavioural responses. According to the unidimensional model, these responses are integrated within a coping style: proactive individuals (bold, active-explorative and social) have a lower hypothalamic–pituitary–adrenal (HPA) axis reactivity than reactive ones (shy, less active-explorative, less social). These associations may change when individuals are exposed to human-induced rapid environmental change (HIREC), such as the introduction of invasive alien species (IAS). Here, we studied Eurasian red squirrels to investigate the relationship between personality traits and one integrated measure of HPA axis activity, both in areas uncolonized (natural populations) and colonized by an IAS, the Eastern grey squirrel (invaded populations). We expected an association between physiological and behavioural responses, and that activity, exploration and social tendency would covary, forming a behavioural syndrome in natural populations, while competition with the IAS was predicted to disrupt these associations. We used faecal glucocorticoid metabolites (FGMs) as an integrated measure of adrenocortical activity, and measured the levels of four personality traits (exploration, activity, activity-exploration and social tendency) with an open field test and a mirror image stimulation test. We found no correlation between FGMs and personality traits, neither in natural nor invaded populations. However, we found correlations among personality traits in areas without interspecific competition, indicating a behavioural syndrome, which was disrupted in invaded populations. This is one of the few studies showing that an IAS, acting as an environmental stressor, alters a native species' behavioural syndrome, but does not influence its coping style.