Burnout in healthcare workers (HCWs) is defined as a state of emotional, physical, and mental exhaustion that results from unmanaged, excessive, and long-term workplace stressors. This study aims to assess the prevalence of burnout and the levels of anxiety and depression among HCWs who primarily work with children who have autism spectrum disorder (ASD). A quantitative cross-sectional survey was conducted utilizing the Arabic version of the Maslach Burnout Inventory (MBI), Areas of Worklife Survey (AWS), Patient Health Questionnaire for Generalized Anxiety Disorder (GAD-7), and Patient Health Questionnaire for Depression (PHQ-9). Among the 381 participants working in autism centers, the majority were young Saudi females (326) working full-time as specialists in the private sector with less than five years of experience. The HCWs’ overall mean scores on the three Maslach Burnout Inventory (MBI) subscales: emotional exhaustion (EE), depersonalization (DP), and personal accomplishment (PA) were 62%, 23.7%, and 76.5%, respectively. A total of 51.4% of HCWs reported moderate to high anxiety levels on GAD-7, and 47.8% showed moderate to very high levels of depression on PHQ-9. The mean perceived EE converged significantly but negatively on their overall mean perceived satisfaction with AWS (p-value < 0.001), demonstrating that greater emotional fatigue predicts less satisfaction with their work. The PA scores correlated significantly and positively with their overall mean satisfaction with their AWS score (p-value < 0.001). Considering sociodemographic variables, HCWs aged between 20–29 years have significantly lower mean PA scores than HCWs aged thirty and older (p = 0.007). Also, male HCWs perceived significantly higher work-related DP than females. More research is required to determine the nature of variables that contribute to burnout, depression, and anxiety in HCWs helping children with ASD.