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Mendelian randomization (MR) has been increasingly used to strengthen causal inference in observational epidemiology. Methodological developments in the field allow detecting and/or adjusting for different potential sources of bias, mainly bias due to horizontal pleiotropy (or “off‐target” genetic effects). Another potential source of bias is nonrandom matching between spouses (i.e., assortative mating). In this study, we performed simulations to investigate the bias caused in MR by assortative mating. We found that bias can arise due to either cross‐trait assortative mating (i.e., assortment on two phenotypes, such as highly educated women selecting taller men) or single‐trait assortative mating (i.e., assortment on a single phenotype), even if the exposure and outcome phenotypes are not the phenotypes under assortment. The simulations also indicate that bias due to assortative mating accumulates over generations and that MR methods robust to horizontal pleiotropy are also affected by this bias. Finally, we show that genetic data from mother–father–offspring trios can be used to detect and correct for this bias.