Sun-induced chlorophyll fluorescence (SIF) has recently been used for the early detection of plant stress. The response of SIF to water stress is complicated by the combination of physiological and non-physiological dynamics in SIF variations and has not been well explored. This paper aims to explore the physiological and non-physiological responses of SIF under different levels of water stress, by analyzing the data from winter wheat with four irrigation treatments (well-watered, moderate, severe, and extreme water stresses). Here the near-infrared radiance of vegetation (NIRvR) and the canopy near-infrared reflectance of vegetation multiplied by incoming sunlight (NIRvP) were selected to represent the non-physiological information of SIF. Then the physiological information (fluorescence yield, ΦF) was extracted by dividing SIF by NIRvP or NIRvR. The results indicate that the physiological and nonphysiological components of SIF were effective indicators for water stress detection. Compared to NDVI, the physiological and non-physiological components exhibited faster responses to different levels of water stress. The non-physiological component explored 68%-77% of SIF under different levels of water stress, and its contributions were firstly decreased and then increased as water stress increased. The stress-induced physiological decrease explored ~50% of SIF decrease under severe water stress and exceeded the non-physiological decrease at the onset of extreme water stress. This study provides direct insights into the physiological and non-physiological dynamics of SIF under different levels of water stress, which contribute to improving the detection of plant stress using SIF.