Stress is a natural response of the body to threatening and challenging situations. Although stress can sometimes have positive impacts, such as enhanced alertness and improved performance, it can also cause harmful effects, such as sustained high blood pressure, anxiety, and depression, especially when prolonged. Continuous monitoring of stress-related molecules, known as stress biomarkers, could enable early diagnosis of stress conditions and therefore improve recovery and reduce healthcare costs and long absences from work. We present a highly sensitive grating-coupled surface plasmon resonance (SPR) sensor for detecting stress biomarkers. The gold-coated sensor chip operates with a tunable laser within the wavelength range of 1527 to 1565 nm. This sensing method is based on detecting a shift of the SPR wavelength, which occurs due to a change in the refractive index of the medium that is caused by the presence of analytes near the plasmonic grating. The sensor chip was tested with four stress-related biomarkers: glucose, creatinine, lactate, and cortisol. With the current version of the sensor, containing no recognition element, the achieved detection limits for these analytes were 5.9, 7.1, 36.9, and 10.7 mM, respectively, which are close to the physiological values of these analytes in body fluids, such as sweat. This proof-of-concept work demonstrates the sensitivity and physiologically relevant detection limits of the presented compact sensor chip and its potential for future healthcare applications, such as continuous stress monitoring, when developed further.