A common challenge in home-based rehabilitation is muscle compensation induced by pain or fatigue, where patients with weakened primary muscles recruit secondary muscle groups to assist their movement, causing issues such as delayed rehabilitation progress or risk of further injury. In a home-based setting, the subtle compensatory actions may not be perceived since physiotherapists cannot directly observe patients. To address this problem, this study develops a novel wearable strain sensor-based shoulder patch to detect fatigue-induced muscle compensation during bicep curl exercises. Built on an observation that the amplitude of a strain sensor's resistance is correlated to the motion of a joint that the sensor is attached to, we develop an algorithm that can robustly detect the state when significant changes appear in the shoulder joint motion, which indicates fatigue-induced muscle compensation in bicep curls. The developed shoulder patch is tested on 13 subjects who perform bicep curl exercises with a 5 kg dumbbell until reaching fatigue. During the experiment, the performance of the shoulder patch is also benchmarked with optical tracking sensors and surface electromyography (sEMG) sensors. Results reveal that the proposed wearable sensor and detection methods effectively monitor fatigue-induced muscle compensation during bicep curl exercises in both Real-Time and Post Hoc modes. This development marks a significant step toward enhancing the effectiveness of home-based rehabilitation by providing physiotherapists with a tool to monitor and adjust treatment plans remotely.