The automated classification of fetal health from cardiotocographic (CTG) recordings is a crucial machine learning application in obstetric diagnostics. Although centralized predictive models have advanced significantly, their large-scale clinical deployment remains structurally constrained by institutional data privacy regulations, data silos, and significant distributional heterogeneity across different recording equipment. To address these interconnected challenges, this study introduces a novel Criticality-Aware Federated Learning framework with Hierarchical Edge Aggregation, designated as FedCrit-HEA. The primary architectural novelty of this framework lies in its two-tier hierarchical federated topology combined with an adaptive optimization layer. Hospital clients optimize local parameters independently and transmit differentially private gradients to regional edge servers for preliminary aggregation, which systematically isolates wide-area network bottlenecks. Crucially, the framework introduces a novel criticality-aware global aggregation mechanism that dynamically adjusts client parameter contributions based on a pathological-sample density metric derived from localized class-distribution statistics. This targeted operator inherently prevents the suppression of clinically critical minority-class gradient information by normal-class dominant clients, which is a persistent limitation in standard federated averaging. Validated across two distinct clinical repositories—the UCI Cardiotocography and the CTU-CHB Dataset—the framework achieves a global macro-averaged F1-score of 0.904 and a pathological-class recall of 84.2% on the UCI partition, alongside an F1-score of 0.901 and a pathological recall of 85.6% on the CTU-CHB data. Simultaneously, the hierarchical edge-aggregation layout reduces wide-area network communication overhead by up to 75% compared to conventional flat federated configurations. These outcomes demonstrate the feasibility and architectural robust novelty of collaborative, privacy-preserving, and minority-sensitive diagnostic modeling within distributed healthcare ecosystems.