Optical fiber sensors have emerged as vital tools in various applications. Among them, Fabry-Perot interferometers (FPIs), have gained prominence due to their compactness and versatility in sensor design. Microwave photonics (MWP) techniques offer enhanced performance and flexibility for developing optical sensor interrogation methods. This paper proposes and experimentally demonstrates a novel MWP interrogation technique based on phase measurement for short-cavity FPI sensors. The technique utilizes the phase response of the FPI sensor within an MWP-assisted single radio frequency bandpass filter, providing improved sensitivity and dynamic sensing capabilities compared to traditional methods. Simulation and experimental results validate the effectiveness of the proposed technique in measuring both static and dynamic strains. The high sensitivity of the system, surpassing 0.00217 rad/μϵ, enables achieving a high resolution better than 100 nϵ at an operating frequency of 247.0 MHz. Additionally, the feasibility of using the technique for interrogating multiplexed FPIs with different cavity lengths is explored, showing promising results for future sensor development.