Previous research in Ethiopia mainly contemplated studying children’s mental distress and the negative effects of orphanages. However, there is a dearth of documented evidence on how positive psychological resources, social support, basic needs services, and mental health impact the well-being of children in childcare institutions and how care centers can benefit vulnerable children. This study aimed to investigate the direct impact of perceived social support (PSS), basic need services (BNS), and Psychological Capital (PsyCap) on the mental health of children in childcare settings. Additionally, the study sought to explore the mediating role of PsyCap between PSS, BNS, and children’s positive mental health (PMH). A total of 420 institutionalized Ethiopian children, comprising 187 females and 233 males, were selected by using a stratified multistage random sampling approach. Validated and standardized measures of psychological well-being (PWB), PsyCap, BNS, and PSS were employed to collect data from the study participants. The findings from the structural equation modeling (SEM) analysis revealed that BNS and PsyCap directly and significantly predicted the PMH of children. Moreover, both BNS and PSS exhibited a positive and significant effect on the higher-order PsyCap construct. Although PSS did not directly influence positive mental health, it indirectly predicted mental health outcomes through the presence of PsyCap. Furthermore, PsyCap played a mediating role between BNS and positive mental health outcomes. It is recommended that future research replicate and expand upon the current study’s findings to gain insights into the positive mental health of institutionalized children.