Polarization maintaining optical fiber (PMOF) is a kind of special optical fiber that is designed to transmit the linearly polarized light. Unlike the general optical fiber, it is critical to conduct the rotational alignment between two PMOFs to guarantee the efficiency of light transmission. Until now, this alignment task still cannot be addressed with an efficient and economical way. Hence, we propose a monolithically integrated two-axis flexure-based microgripper that has the grasping and rubbing functions. To achieve a compact structure, the microgripper is designed with an asymmetric architecture. In this paper, the pseudo-rigid body model approach and finite element analysis are conducted to provide the essential guideline to accomplish the theoretical design. The prototype is fabricated by wire electrical discharge machining, with which two experiments are conducted to validate the performance of the microgripper. The experimental results demonstrate that the proposed microgripper can firmly grasp the optical fiber with the diameter of 250 μm and meanwhile can rub it more than 90° accurately and effectively, which indicate that it can satisfy the operating requirements well in the PMOF assembly.