In encoderless Model Predictive Torque Control (MPTC) of three-phase Induction Motor (IM) drives, current sensors can face different electrical or mechanical faults in harsh industrial environments. In this research, single-phase current sensor Fault-Tolerant Control (FTC) method for MPTC of three-phase IM drives without speed measurement using a flux linkage observer and Model Reference Adaptive System (MRAS) algorithm is proposed. In the presented FTC method, Third-Difference (TD) operators, logic circuit module, flux linkage observer, and MRAS algorithm are utilized for fault detection, fault isolation, estimation of stator currents and fluxes, and speed estimation, respectively. In comparison with the conventional current sensor FTC methods, the proposed method can be utilized for encoderless three-phase IM drives. In order to confirm the usefulness and possibility of the proposed encoderless FTC method, experimental studies are performed for a 0.75 kW three-phase IM drive system in different situations. The achieved results demonstrate good performances of the proposed technique during both normal and faulty situations.