In present study, a novel coupling phase shift detection technology of a single-mode fiber coupler based on the hybrid Sagnac interferometer is proposed. According to the valley wavelength characteristics of its reciprocal port and non-reciprocal port output spectra, the detection of the coupling phase shift of the single-mode fiber coupler is realized, and the detection accuracy can reach 0.0136°, which is an order of magnitude higher than the existing coupling phase shift detection accuracy (0.229°). The experimental system is built to realize the detection of the coupling phase shifts of 3×3 single-mode coupler with the fixed splitting ratio and 2×2 single-mode couplers with different splitting ratios. The detection results are consistent with theoretical estimates, and the maximum standard deviation of multiple detection is 0.0036°. The proposed detection method is also used to measure the coupling phase shift change of the 2×2 single-mode coupler at different temperatures for the first time. The research shows that the proposed detection method has advantages in simplicity, detection accuracy, and adaptability. It can be used for the quantitative and accurate measurement and analysis of coupling phase shift of various multi-port single-mode fiber couplers, and provides an important technical support for the development and screening of phase stabilizer couplers.