Many studies have examined the average effects of ocean acidification and warming on phenotypic traits of reef fishes, finding variable, but often negative effects on behavioural and physiological performance. Yet the presence and nature of a relationship between these traits is unknown. A negative relationship between phenotypic traits could limit individual performance and even the capacity of populations to adapt to climate change. Here, we examined the relationship between behavioural and physiological performance of a juvenile reef fish under elevated CO2 and temperature in a full factorial design. Behaviourally, the response to an alarm odour was negatively affected by elevated CO2, but not elevated temperature. Physiologically, aerobic scope was significantly diminished under elevated temperature, but not under elevated CO2. At the individual level, there was no relationship between behavioural and physiological traits in the control and single-stressor treatments. However, a statistically significant negative relationship was detected between the traits in the combined elevated CO2 and temperature treatment. Our results demonstrate that trade-offs in performance between behavioural and physiological traits may only be evident when multiple climate change stressors are considered, and suggest that this negative relationship could limit adaptive potential to climate change.