This article proposes a fiber Bragg grating (FBG)-based high-precision sensor for cardiovascular pulse monitoring in real time. The sensor prototype mainly consists of a force-sensitive flexure in a parallel structure configuration, a suspended optical fiber inscribed with an FBG element, a contact pad, and a wearable elastic band. The proposed flexure develops from a six-bar parallel mechanism based on the rigid-body replacement method and achieves a compact, miniatured, and wearable design. This flexure converts the longitudinal pulse input into a horizontal deformation/force output, supports the force amplification with a simplified bridge-type amplified mechanism, and achieves the improved sensitivity of pulse waveform measurement. The FBG optical fiber has been horizontally suspended and assembled on the flexure with a two-point pasting configuration and sensed the horizontal stretching and compression-induced strain variation. The parallel flexure based on a dual design has been introduced to depress the crosstalk among the lateral directions and the influences of external measurement disturbances. Design optimization has been performed based on the finite element method (FEM) simulation to improve the sensor sensitivity. Both static and dynamic experiments verify the performances of the optimized wearable sensor design. The sensor sensitivity achieves an excellent sensitivity of 1547.3 pm/N with a small linearity error of 0.38% and negligible crosstalk of less than 2% in radial directions, validating its negligible antiturbulence capability. The proposed sensor design also supports the easy implementation of the handheld sensor form. The carotid pulse measurement experiments for both the wearable and handheld sensor forms were carried out to validate the effectiveness of the proposed sensor design.