The independent effects of smoking and alcohol in head and neck cancer are not clear, given the strong association between these risk factors. Their apparent synergistic effect reported in previous observational studies may also underestimate independent effects. Here we report multivariable Mendelian randomization performed in a two-sample approach using summary data on 6,034 oral/oropharyngeal cases and 6,585 controls from a recent genome-wide association study. Our results demonstrate strong evidence for an independent causal effect of smoking on oral/oropharyngeal cancer (IVW OR 2.6, 95% CI = 1.7, 3.9 per standard deviation increase in lifetime smoking behaviour) and an independent causal effect of alcohol consumption when controlling for smoking (IVW OR 2.1, 95% CI = 1.1, 3.8 per standard deviation increase in drinks consumed per week). This suggests the possibility that the causal effect of alcohol may have been underestimated. However, the extent to which alcohol is modified by smoking requires further investigation.