The growing reliance on telehealth and Internet of Medical Things (IoMT) technologies has improved healthcare accessibility but exposed patient data and clinical operations to cybersecurity threats, including unauthorized access, spoofing, and data alteration attacks. Conventional cloud-based intrusion detection systems (IDS) are unsuitable for telehealth environments because they introduce latency, bandwidth overhead, and privacy risk. This study proposes an Edge-Optimized Deep Neural Network integrated with Marine Predators Algorithm feature selection (EO-DNN-MPA) for real-time intrusion detection in telehealth systems. The model was trained and evaluated on the WUSTL-EHMS-2020 healthcare cybersecurity dataset following preprocessing, class balancing, and feature optimization that reduced dimensionality from 36 to 16 features. Three model configurations were evaluated: the original EO-DNN-MPA, a pruned version, and a pruned-and-quantized version. The original model achieved 95.33% accuracy, 93.15% precision, 97.85% recall, 95.44% F1-score, 99.29% AUC, and an inference time of 1.1101 ms. The pruned-and-quantized model maintained comparable detection performance, 95.12% accuracy, 93.20% precision, 97.34% recall, 95.22% F1-score, and 99.25% AUC, while reducing inference time to 0.6679 ms, a 39.8% latency reduction. The proposed model outperformed comparable state-of-the-art approaches evaluated on the same dataset, including federated DNN, ensemble boosting, and explainable XGBoost methods. The results demonstrate that combining edge-aware architectural design, pruning, and quantization with deep learning yields an efficient, privacy-preserving, and low-latency intrusion detection solution suitable for real-time telehealth security applications.