Background Associations of anxiety disorder and depression with coronary artery disease (CAD) are heterogeneous between populations. This study investigated how genetic susceptibility to CAD alters these associations with incident CAD, comparing and combining anxiety disorder and depression. Methods This is a prospective cohort study using UK Biobank. Diagnoses of anxiety disorder and depression were ascertained through linked hospital admission data. Incident CAD was ascertained through hospital admission and death certificate data after baseline. CAD polygenic risk score (PRSCAD) was obtained from CARDIoGRAMplus4 and categorised into low, intermediate, and high. Cox proportional hazard models were used to examine associations between anxiety disorder and depression and CAD. Results Both anxiety disorder (HR 2.31, 95% CI 1.92–2.78) and depression (HR 2.15, 95% CI 1.90–2.24) were associated with CAD after adjusting for sociodemographic confounders. There was an addictive interaction between depression and PRSCAD (RERI 0.97, 95% CI 0.12–1.81) such that the association between depression and CAD was strongest among those with a high PRSCAD whilst there was no such evidence for anxiety disorder. Anxiety disorder only (HR 1.68, 95% 1.16–2.44), depression only (HR 2.13, 95% CI 1.72–2.64), and concomitant anxiety disorder and depression (HR 3.85, 95% CI 2.48–5.98) were associated with CAD even among people with a low PRSCAD. Adjusting for potential mediators attenuated all these associations across PRS categories. Conclusions CAD genetic susceptibility might partly contribute to the clustering of depression and CAD but does not provide a full explanation, nor does it explain the association between anxiety disorder and CAD. Therefore, other mechanisms should be explored.