Background: Causes of the association between lower cognitive ability and poorer health remain unknown, but may reflect a shared genetic aetiology as indicated by previous research. This study examines the causal genetic associations between cognitive ability and physical health outcomes. Method: We carried out Mendelian randomization analyses using the inverse variance weighted method to test for causality between later life cognitive ability, educational attainment (as a proxy for cognitive ability in youth), BMI, height, systolic blood pressure, coronary artery disease, and type 2 diabetes in the UK Biobank sample (N = 112 151). Sensitivity analyses were performed using MR-Egger regression. Results: BMI, systolic blood pressure, coronary artery disease and type 2 diabetes showed negative associations with cognitive ability, while height was positively associated with cognitive ability. The Mendelian randomization analyses provided no evidence for a casual association from health to cognitive ability. In the other direction, higher educational attainment predicted lower BMI, systolic blood pressure, coronary artery disease, type 2 diabetes, and taller stature. The Mendelian randomization analyses indicated partly causal associations from educational attainment to health, however when adjusting for bias using the MR-Egger regression, these effects disappeared. Conclusions: The lack of consistent evidence for causal associations between cognitive ability, educational attainment, and physical health could be explained by violations of the Mendelian randomization assumptions, including biological pleiotropy.