Background: Early childhood caregivers are exposed to intensive caregiving demands and have a high risk of depression. Guided by the family stress process model and Acceptance and Commitment Therapy (ACT), this cross-sectional study examined whether psychological flexibility mediates the association between parenting stress and depression. Methods: A cross-sectional survey was conducted among 1140 Chinese primary caregivers of infants aged 0–36 months in Ya’an, Sichuan, China, from 9 October 2022 to 8 October 2025 using convenience sampling. Validated scales included the Parenting Stress Index-Short Form (PSI-SF), Acceptance and Action Questionnaire-II (AAQ-II) (Higher AAQ-II scores reflected lower psychological flexibility), and Patient Health Questionnaire-8 (PHQ-8). Hayes’ PROCESS Model 4, with 5000 bootstrap resamples, was adopted for the mediation analysis. Results: Parenting stress was positively associated with depressive symptoms (r = 0.335, p < 0.01) (weak-to-moderate effect size). Psychological flexibility exerted a partial mediating effect between the two variables, and the indirect effect accounted for 45% of the total effect. Caregivers with lower household income, lower educational level, and those caring for children aged 0–12 months reported significantly higher depression (all p < 0.05). Conclusions: Parenting stress is an important risk factor for depression, and psychological flexibility plays a significant partial mediating role in this relationship. ACT-based interventions targeting psychological flexibility may hold implications for depression among early childhood caregivers.