To address the torque ripple and speed fluctuation issues in high-frequency square-wave injection-based sensorless control of interior permanent magnet synchronous motors (IPMSM) caused by low-order stator current harmonics (primarily the fifth and seventh), this paper proposes a harmonic voltage compensation strategy based on a sixth-order quasi-proportional resonant (QPR) controller, which effectively suppresses these specific harmonic disturbances. The proposed method, building upon conventional high-frequency square-wave injection, introduces a harmonic current extraction technique based on multiple synchronous reference frame transformations to separate the fifth and seventh harmonic components accurately; then, according to the established harmonic voltage compensation equation, generates targeted compensation voltage commands; finally, further precisely suppresses the corresponding harmonic currents through a sixth-order QPR controller connected in parallel with the current proportional-integral (PI) controller. This paper comprehensively establishes the mathematical models for harmonic extraction and voltage compensation, and conducts a detailed analysis of the parameter design of the sixth-order QPR controller. Simulation results demonstrate that the proposed strategy can significantly suppress stator current distortion, effectively reduce torque and speed ripples, and substantially improve rotor position estimation accuracy, thereby verifying the superiority of the novel harmonic-suppression-based sensorless control strategy.