In recent years, networked IoT systems have revolutionized connectivity, portability, and functionality, offering a myriad of advantages. However, these systems are increasingly targeted by adversaries due to inherent security vulnerabilities and limited computational and storage resources. Malicious applications, commonly known as malware, pose a significant threat to IoT devices and networks. While numerous malware detection techniques have been proposed, existing approaches often overlook the resource constraints inherent in IoT environments, assuming abundant resources for detection tasks. This oversight is compounded by ongoing workloads such as sensing and on-device computations, further diminishing available resources for malware detection. To address these challenges, we present a novel resource- and workload-aware malware detection framework integrated with distributed computing for IoT networks. Our approach begins by analyzing available resources for malware detection using a lightweight regression model. Depending on resource availability, ongoing workload executions, and communication costs, the malware detection task is dynamically allocated either on-device or offloaded to neighboring IoT nodes with sufficient resources. To safeguard data integrity and user privacy, rather than transferring the entire malware detection task, the classifier is partitioned and distributed across multiple nodes, and subsequently integrated at the parent node for comprehensive malware detection. Experimental analysis demonstrates the efficacy of our proposed technique, achieving a remarkable speed-up of 9.8x compared to on-device inference, while maintaining a high malware detection accuracy of 96.7%.