Background: Improving the labor productivity of small and medium-sized enterprises (SMEs) is essential because of the aging population and predicted reduction in the labor force. Therefore, it is necessary to ensure that employees are in good health to work for long times. In this regard, the purpose of the study is to investigate the relationship between work engagement (WE) and related variables among SME employees. Methods: A cross-sectional study was conducted using the baseline data of the prospective cohort study, which included 377 employees from three SMEs headquartered in Hiroshima Prefecture, Japan. Results: A multiple regression analysis was performed to see the associations between Utrecht Work Engagement Scale (UWES) scores and other variables. Significant associations were found with job satisfaction, age, health literacy (HL), and quality of sleep (all, p < 0.05). Additionally, there was a statistically significant difference observed in WE, quality of sleep, concern for own body, job satisfaction, and family life satisfaction (all, p < 0.001) with respect to high and low HL levels. Conclusions: The results of this study reveal that while implementing health and productivity management in SMEs to increase WE, it is best to concentrate on raising HL, job satisfaction, and sleep quality. To increase generalizability, further research could be conducted with more SMEs companies.