Introduction Previous studies reported that parents of children with autism spectrum disorder (ASD) experience higher levels of stress than parents of children with typical development. Methods This study conducted a quantitative cross-sectional survey to evaluate the levels of depression, anxiety, and stress among mothers of children with ASD compared with mothers of children with typical development. In addition, we assessed whether the perception of social support is correlated to psychological well-being. The study recruited a non-probability sample of 143 mothers of children with ASD and a comparison group of 143 mothers of children with typical development. For data collection, an online questionnaire was used to investigate the levels of depression, anxiety, and stress using the 21-item Depression Anxiety Stress Scale (DASS-21) and examine social support for mothers using the Multidimensional Scale of Perceived Social Support (MSPSS). Results No significant difference was observed in the levels of depression and anxiety between both groups. Nevertheless, extremely severe levels of depression and anxiety were observed in 23.1% and 27.3% of mothers in the ASD group compared with 11.9% and 16.8% for the control group, respectively. Alternatively, a significant difference exists between the two groups in the levels of stress. Extremely severe stress was identified in 17.5% of mothers of children with ASD compared with only 6.3% in the control group (p = 0.04). Lastly, the study found a significant correlation among the scores for stress, anxiety, and depression and for MSPSS. Conclusion Providing mental health services for mothers in need and investigating the underlying factors of extremely severe levels of depression and anxiety are recommended initiatives.