Evidence on whether menopausal hormone therapy (MHT) affects neurological or psychiatric disease is conflicting. As MHT acts by binding to oestrogen receptors (ERα and ERβ), we used drug-target Mendelian randomisation (MR) to test whether perturbing these targets alters the risk of Alzheimer's disease (AD), brain structure, depression, or anxiety. Genetic variants in the genes encoding these oestrogen receptors (ESR1 and ESR2) that were associated with positive controls were leveraged as instrumental variables. In two-sample MR analyses using large genome-wide association studies, genetically proxied ERα and ERβ perturbation showed no evidence of effect on AD or on cortical grey matter, hippocampal volume, or white matter hyperintensities. Genetically proxied ERβ perturbation significantly increased risk for depression (β = -0.66, 95% CI [-0.99, -0.32], p = 0.002), but not anxiety. Our study highlights psychiatric considerations when targeting oestrogen receptors with MHT, but provides no evidence for either harmful or protective effects on AD risk.