Recent advancements in conductive yarns and fabrication technologies offer exciting opportunities to design and knit seamless garments equipped with sensors for biomedical applications. In this paper, we discuss the design and application of a wearable strain sensor, which can be used for biomedical monitoring such as contraction, respiration, or limb movements. The system takes advantage of the intensity variations of the backscattered power (RSSI) from an inductively-coupled RFID tag under physical stretching. First, we describe the antenna design along with the modeling of the sheet impedance, which characterizes the conductive textile. Experimental results with custom fabricated prototypes showed good agreement with the numerical simulation of input impedance and radiation pattern. Finally, the wearable sensor has been applied for infant breathing monitoring using a medical programmable mannequin. A machine learning technique has been developed and applied to post-process the RSSI data, and the results show that breathing and non-breathing patterns can be successfully classified.