Induction motors are essential and widely used components in many industrial processes. Although these machines are very robust, they are prone to fail. Nowadays, it is a paramount task to obtain a reliable and accurate diagnosis of the electric motor health, so that a subsequent reduction of the required time and repairing costs can be achieved. The most common approaches to accomplish this task are based on the analysis of currents, which has some well-known drawbacks that may lead to false diagnosis. With the new developments in the technology of the sensors and signal processing field, the possibility of combining the information obtained from the analysis of different magnitudes should be explored, in order to achieve more reliable diagnostic conclusions, before the fault can develop into an irreversible damage. This paper proposes a smart-sensor that explores the weighted analysis of the axial, radial, and combination of both stray fluxes captured by a low-cost, easy setup, non-invasive, and compact triaxial stray flux sensor during the start-up transient through the short time Fourier transform (STFT) and characterizes specific patterns appearing on them using statistical parameters that feed a feature reduction linear discriminant analysis (LDA) and then a feed-forward neural network (FFNN) for classification purposes, opening the possibility of offering an on-site automatic fault diagnosis scheme. The obtained results show that the proposed smart-sensor is efficient for monitoring and diagnosing early induction motor electromechanical faults. This is validated with a laboratory induction motor test bench for individual and combined broken rotor bars and misalignment faults.