In this paper, an in-line Mach-Zehnder interferometer embedded in a fiber Bragg grating (FBG) is fabricated by a tiny offset-core splicing technique and inserted into a fiber ring laser to effectively improve the detection limit and discrimination of sensing. Through fine power adjustment, the stable operation of dual-wavelength lasing is completed in a single FBG for the first time to our knowledge, and simultaneous measurement of refractive index (RI) and ambient temperature is achieved with high discrimination due to the RI immunity of the FBG. The experimental results indicate that the sensitivities of RI and temperature are -30.57 nm/RIU and 131.1 pm/°C, respectively, with very low intensity drift. Furthermore, the over 20 times improvement of the RI detection limit is obtained owing to the large extinction ratio (>30 dB) and small linewidth (≤0.13 nm).