The increasing connectivity of Internet of Medical Things (IoMT) devices has accentuated their susceptibility to cyberattacks. The sensitive data they handle makes them prime targets for information theft and extortion, while outdated and insecure communication protocols further elevate security risks. This paper presents a lightweight and innovative approach that combines Benford’s law with statistical distance functions to detect attacks in IoMT devices. The methodology uses Benford’s law to analyze digit frequency and classify IoMT devices traffic as benign or malicious, regardless of attack type. It employs distance-based statistical functions like Jensen-Shannon divergence, Kullback-Leibler divergence, Pearson correlation, and the Kolmogorov test to detect anomalies. Experimental validation was conducted on the CIC-IoMT-2024 benchmark dataset, comprising 45 features and multiple attack types. The best performance was achieved with the Kolmogorov test ( \(\alpha = 0.01\) ), particularly in DoS ICMP attacks, yielding a precision of \(99.24\%\) , a recall of \(98.73\%\) , an F1 score of \(98.97\%\) , and an accuracy of \(97.81\%\) . Jensen-Shannon divergence also performed robustly in detecting SYN-based attacks, demonstrating strong detection with minimal computational cost. These findings confirm that Benford’s law, when combined with well-chosen statistical distances, offers a viable and efficient alternative to machine learning models for anomaly detection in constrained environments like IoMT.