Burnout can affect nurses’ sleep quality. The aim of this study was to analyze the relationship between burnout syndrome and sleep problems in nurses. A systematic review with meta-analysis was performed. PubMed, CINAHL and Scopus databases were used. Some of the inclusion criteria were quantitative studies, in which the levels of burnout and sleep disorders were investigated in a sample of nurses using validated scales. A total of 12 studies were included. Sociodemographic variables did not influence the relation between burnout and sleep problems, except for being female. The environment and workplace violence, together with psychological traits and shifts, affect the probability of developing burnout and insomnia. The meta-analysis sample was n = 1127 nurses. The effect size of the correlation between burnout and sleep disorders was r = 0.39 (95% CI 0.29–0.48) with p < 0.001, indicating that the higher the level of burnout in nurses, the greater the presence of sleep disorders. The positive correlation between burnout and sleep disorders is a problem that must be addressed to improve the health of nurses. Developing turnicity strategies, using warmer lights in hospital units during night shifts and eliminating the fixed night shift could improve nurses’ working conditions.