In this paper, a non-tunable fiber Fabry-Perot filter (FFPF) is configured to demodulate dynamic strain signals in a multiplexed dynamic sensing system based on a fiber ring laser. A semiconductor optical amplifier (SOA) contained in the fiber ring laser cavity enables this system to implement multiplex operation because of the inhomogeneous broadening of the SOA source. The shift of the reflective spectrum of the fiber Bragg grating caused by external dynamic strain is demodulated by the FFPF in the laser cavity, which ultimately generates an amplified output. In the experiment, the sensing system can respond to dynamic strains at ultra-high frequencies up to megahertz, and an example for detection of ultrasonic signals in water has been successfully demonstrated. A dual-channel system for multiplexing demodulation is also discussed. This system presented here has a simple structure and a low cost, which makes it attractive for dynamic strain detection in structural health monitoring.