(1) Pediatric inflammatory multisystem syndrome (PIMS) is a relatively rare complication of coronavirus disease (COVID-19). So far, it is unclear why COVID-19 in children has usually mild or asymptomatic courses, whereas PIMS, which develops several weeks after COVID-19, is a serious life-threatening condition. (2) In this proof-of-concept study, using the ELISA method, we compared selected clinical and immunological parameters in small groups of children with PIMS and COVID-19. Children with various inflammatory diseases were included as a control. (3) Patients with PIMS revealed significantly higher levels of pro-inflammatory molecules (C-reactive protein and IL-6) and markers of heart injury (troponin I and N-terminal prohormone of brain natriuretic peptide) as compared to other groups. Moreover, these markers correlated with increased levels of soluble receptors for tumor necrosis factor (sTNF-R1 and sTNF-R2). (4) Our observation may be a step forward to better understand the phenomenon of mild COVID-19 in children and its severe complications in PIMS. It is hypothesized that the delayed inflammation results in excessive cardiomyocyte damage and the release of sTNF-R1 and -R2. Therefore, possibly the involvement of the TNF pathway in PIMS could be explored as a potential therapeutic target. However, further studies are required to validate this approach.