Fiber Bragg gratings (FBGs) are excellent tools for monitoring mechanical and thermal strains, and have widespread application in the structural health monitoring (SHM) of aerospace, civil, and mechanical structures. A common approach used for interrogating FBG sensors involves the illumination of the sensor with a broadband laser source and the narrowband reflected light reflected from the FBG is monitored with a wavelength sensitive optical detection system. The thermal or mechanical perturbations experienced by the FBG sensor lead to a shift in its reflectivity spectrum. In this work, an alternative interrogation scheme is presented that uses an FBG based narrowband tunable laser source produced by incorporating the FBG into a fiber ring laser cavity as an optical feedback element. The laser cavity consists an erbium doped fiber (EDF) connected to the FBG at the output of the fiber ring, which allows for the generation of the required amplified stimulated emission (ASE) in the C-band and lasing at the center wavelength of the FBG reflectivity spectrum. With this interrogation scheme, the wavelength of the resulting narrowband laser source tracks the center wavelength of the FBG sensor as it drifts due to quasi-static and/or dynamic mechanical and thermal strains. In addition, the instantaneous spectral line-width of the laser source is effectively narrowed owing to the long length of the laser cavity, which facilitates highly sensitive demodulation of dynamic shifts of the lasing wavelength with a high coherence optical interferometer. In this paper, experimental results are presented that illustrate the monitoring of strain induced quasi-static and dynamic shifts of the wavelength of the tunable laser in both single and multiple FBG sensor configurations. The quasi-static wavelength shifts are monitored with a spectrum analyzer while a path stabilized Michelson interferometer is used to demodulate the dynamic wavelength shifts.