Background: This study aims to assess whether the associations between burnout and sick leave due to stress-related mental disorders, other mental disorders, and somatic conditions are influenced by familial (genetic and shared environmental) factors. Methods: In this prospective cohort study, 23,611 Swedish twins born between 1959 and 1985, who answered a web-based questionnaire, including the Pines Burnout Measure 2004–2006, were included. Registry data on sick leave spells from the response date until December 31, 2010 were obtained from the Swedish Social Insurance Agency. Logistic regression analysis was performed to assess odds ratios with 95% confidence intervals for the association between burnout and sick leave for the whole sample, while conditional logistic regression of the same-sex discordant twin pairs was used to estimate the association between burnout and sick leave, adjusting for familial confounding. The Bivariate Cholesky models were used to assess whether the covariation between burnout and sick leave was explained by common genetic and/or shared environmental factors. Results: Burnout was a risk factor for sick leave due to stress-related and other mental disorders, and these associations were explained by familial factors. The phenotypic correlation between burnout and sick leave due to somatic conditions was 0.07 and the association was not influenced by familial factors. The phenotypic correlations between burnout and sick leave due to stress-related (0.26) and other mental disorders (0.30) were completely explained by common genetic factors. Conclusions: The association between burnout and sick leave due to stress-related and other mental disorders seems to be a reflection of a shared genetic liability.