In this work, we have demonstrated the use of a fiber Bragg grating (FBG) sensor to measure the pressure profile of blast waves generated inside a vertical shock tube (VST). An FBG pressure sensor probe has been designed and developed that can be incorporated into the wall of the VST. The VST facility is used to generate blast waves with decay times of the order of a few milliseconds to simulate explosive events. Pressure measurement experiments have been carried out at different incident blast wave peak pressures inside the VST. The FBG pressure sensor measurements are validated against a standard piezoelectric pressure transducer at an acquisition rate of 1 MHz. The pressure signals of both sensors are found to match well with similar rise times and decay profiles. The validated FBG pressure sensor is then incorporated into a sand column mounted in the test section of the VST to measure the pressure profile of blast wave-induced stress waves in granular media. The FBG and piezoelectric pressure sensor data are compared using fast Fourier transform analysis and continuous wavelet transform. The feasibility of FBG sensors for blast pressure measurement under harsh conditions imposed inside shock tube environments is established.