For industry, the induction motors are essential elements in production chains. Despite the robustness of induction motors, they are susceptible to failures. The broken rotor bar (BRB) fault in induction motors has received special attention since one of its characteristics is that the motor can continue operating with apparent normality; however, at certain point the fault may cause severe damage to the motor. In this work, a methodology to detect BRBs using vibration signals is proposed. The methodology uses the Shannon entropy to quantify the amount of information provided by the vibration signals, which changes due to the presence of new frequency components associated with the fault. For automatic diagnosis, the K-means cluster algorithm and a decision-making unit that looks for the nearest cluster through the Euclidian distance are applied. Unlike other reported works, the proposal can diagnose the BRB condition during startup transient and steady state regimes of operation. Additionally, the proposal is also implemented into a field programmable gate array in order to offer a low-cost and low-complex online monitoring system. The obtained results demonstrate the proposal effectiveness to diagnose half, one, and two BRBs.