This letter proposes a short-circuit and over-current fault detection solution for Silicon-Carbide(SiC) MOSFET modules based on tunnel magnetoresistance(TMR). The TMR sensor is integrated into a SiC MOSFET module to noninvasively measure its current. The measured current is compared to a threshold to detect short-circuit and over-current faults. The TMR sensor is installed in a chosen location, where the TMR sensor gain is automatically doubled in the event of short-circuit fault. As a result, a short-circuit fault can be predicted, i.e. the fault is detected before the actual short-circuit current reaches the threshold. Besides, only 1 TMR sensor is required to detect both short-circuit and over-current faults for a half-bridge power module. According to the experimental results, the short-circuit fault is detected when the fault current reaches half of the fault threshold current. The experimental results indicate general superiority over desaturation(DeSat) technology and better performance in detection time, reaction time and total protection time compared to Rogowski switch-current sensor(RSCS)-based technology.