It remains unclear whether the association between obstructive sleep apnoea (OSA), a form of sleep-disordered breathing (SDB), and atrial fibrillation (AF) is causal or mediated by shared co-morbidities such as obesity. Existing observational studies are conflicting and limited by confounding and reverse causality. We performed Mendelian randomisation (MR) to investigate the causal relationships between SDB, body mass index (BMI) and AF. Single-nucleotide polymorphisms associated with SDB (n = 29) and BMI (n = 453) were selected as instrumental variables to investigate the effects of SDB and BMI on AF, using genetic association data on 55,114 AF cases and 482,295 controls. Primary analysis was conducted using inverse-variance weighted MR. Higher genetically predicted SDB and BMI were associated with increased risk of AF (OR per log OR increase in snoring liability 2.09 (95% CI 1.10–3.98), p = 0.03; OR per 1-SD increase in BMI 1.33 (95% CI 1.24–1.42), p < 0.001). The association between SDB and AF was not observed in sensitivity analyses, whilst associations between BMI and AF remained consistent. Similarly, in multivariable MR, SDB was not associated with AF after adjusting for BMI (OR 0.68 (95% CI 0.42–1.10), p = 0.12). Higher BMI remained associated with increased risk of AF after adjusting for OSA (OR 1.40 (95% CI 1.30–1.51), p < 0.001). Elevated BMI appears causal for AF, independent of SDB. Our data suggest that the association between SDB, in general, and AF is attributable to mediation or confounding from obesity, though we cannot exclude that more severe SDB phenotypes (i.e., OSA) are causal for AF.