Objectives: This study analyzed the stress experienced by family caregivers of children with special healthcare needs and identified associated factors. Methods: A case–control study was conducted with the “cases” being caregivers of children with chronic conditions and the “controls” being caregivers of healthy children. Recruitment was carried out via social media and complemented by snowball sampling. A sociodemographic questionnaire and the Perceived Stress Scale were applied, with four saliva samples collected in one day (at 8:00 am, 30 min later, and 4 and 12 h later). The Area Under the Curve for total daily cortisol production was calculated using the log-trapezoidal method. The Wilcoxon test and repeated-measures ANOVA were used for statistical analysis. Results: In total, 100 caregivers participated, with 50 in the “case” group and 50 in the “control” group. Significant differences in stress scores and salivary cortisol levels were observed between the groups, with the other variables constant. In both groups, cortisol levels followed a typical circadian pattern. Family income was associated with perceived stress. Caregiver age significantly explained perceived stress (p = 0.0098) and total cortisol production. Caregiver occupation also influenced cortisol results. Conclusions: Caregivers of children with chronic conditions showed higher perceived stress and lower cortisol production compared to those of healthy children. Family income, occupation, and caregiver age were associated with stress.