Metal-organic frameworks (MOFs) are a class of materials with highly ordered pore structures. Due to their unique physical and chemical properties, they show great potential in the field of biosensors. Some MOFs can adsorb fluorescently labeled nucleic acid aptamers through various interaction mechanisms (such as electrostatic interactions, it-it stacking, hydrogen bonding, etc.). These interactions not only ensure the stable binding of the aptamers but also allow for their controlled release under specific conditions (such as changes in pH, temperature, or the presence of specific molecules). This mechanism provides multiple possibilities for the design of biosensors. Herein, we have systematically compared the quenching effects of widely used MOFs that can bind to aptamers, i.e., Fe-MOF (MIL-101), Cu-MOF, Zn-MOF (ZIF-8) and Zr-MOF (UiO-66). The study on the kinetics, quenching efficiency, and influencing factors such as ionic strength pH and temperature is performed. Interestingly, Cu-MOF exhibits superior quenching abilities to the other three materials in both the quenching efficiency and kinetics. Thus, a Cu-MOF based fluorescent sensor is reported to detect the ovarian cancer marker carbohydrate antigen 125 (CA125), which provides convenient detection performance (assay time about 10 min), and a detection range from 0.1 to 400 ng/mL. Moreover, it is designed in a simple mix-and-detect format and can be directly applied to clinical sample detection. This work may offer guidance for the choice of MOFs and elaborate design of biosensors.