Background/Objectives: Relatives play the main role as caregivers of autism spectrum disorder (ASD) individuals. Women, specifically mothers, are the majority of caregivers of ASD relatives. In addition, the literature on caregivers has shown that women have worse mental health and higher perceived burdens than men. Therefore, the aim of this work was to evaluate the relationships between psychological distress and burden using a gender approach in caregivers of ASD relatives. Methods: A cross-sectional design was applied in this study with a convenience sample of 250 caregivers of ASD relatives. Most of them were mothers caring for a child who ranged in age from 1 to 31 years. Sociodemographic variables considered were age, education level, marital status, and relation to the care recipient. Additionally, psychological distress and objective burden, in the form of hours/day caring, and subjective burden, in the form of perceived burden, were analyzed. Results: Significant gender differences were found in psychological distress and objective and subjective burden, with women showing higher scores than men. Both types of burden played a serial mediating role between gender and psychological distress. Conclusions: The results highlight the important role of gender, with women bearing the high cost of caring for their children with ASD in the form of high objective burden, caring for more hours, and subjective burden, perceiving more burden and showing poorer mental health than men. These results show the need for specific support and intervention programs targeted to women caregivers to reduce burden and improve their mental health.