By using the concept of exceptional point (EP), we propose an efficient optomechanical (OM) mass sensor. The system is constituted by two mechanically coupled OM cavities respectively driven by a blue and a red detuned laser. By engineering the effective mechanical gain and loss, we can reach an EP where any perturbation induces a frequency splitting that scales as the square root of the perturbation strength, resulting in a giant sensitivity factor enhancement compared to the conventional mass sensors. Additionally, to extend our scheme to two non-identical mechanical resonators, we propose to use quadratic OM coupling to tune the mismatch frequency to get closer to the EP. This work paves the way towards new levels of sensitivity for OM sensors including nanoparticles detection, precision measurement, and quantum metrology.