Induction motors, key elements for industry, are susceptible to one or more faults at the same time; yet, they can keep working without affecting the process, but increasing the production costs. For this reason, a monitoring system that can efficiently diagnose the induction motor condition, even under multiple combined faults, is a demanding task. In this work, a methodology and its implementation into a field programmable gate array for an online and real-time monitoring system of multiple combined faults are presented. First, the fractal dimension approach, using the Katz algorithm, is introduced as a measure of variation of 3-axis startup vibration signals for the induction motor condition, considering that these signals describe changes on its dynamic characteristics due to the different faults. Then, an artificial neural network determines in an automatic way the induction motor condition according to the fractal dimension values. The obtained results show a higher overall efficiency than previous works for detecting broken rotor bars, outer-race bearing defects, unbalance, and their combinations, as well as a healthy condition.