This paper proposes a fiber-optic Fabry-Perot pressure sensor based on microelectromechanical systems (MEMS) technology for the measurement of transient pressures, including shock waves. The sensitive unit is composed of etched silicon wafers and BF33 glass wafers by anodic bonding, and the adhesive-free integration of the optical fiber and the sensitive unit is realized by laser fusion bonding technology. A signal demodulation experiment platform was constructed to comprehensively evaluate the pressure sensing characteristics of the sensors in static and dynamic pressure environments. The experimental findings demonstrate that the sensor exhibits a satisfactory linear response within the pressure range of 0-10 MPa, with a full-scale non-linear error of 0.41% and a hysteresis of 0.37%. Furthermore, the sensor demonstrated a rise time of 8.5 μs during dynamic pressure measurements. The sensor has the advantages of anti-electromagnetic interference, high consistency, low cost, and has a theoretical resonant frequency of 1.39 MHz, demonstrating the prospect of its wide application for dynamic pressure measurement in harsh environments such as explosion fields.