The detection and location of eccentricity faults in a permanent magnet synchronous generator (PMSG) become increasingly essential, especially in safety-critical applications. However, the existing approaches for monitoring eccentricity subject to many limitations. In this article, a novel method for online detection and location of the eccentricity fault in a PMSG is proposed based on the external magnetic sensing. The noninvasiveness facilitates installation and maintenance work. In this article, the effect of different eccentricity faults on the external leakage flux density is analyzed theoretically with the magnetic equivalent circuit method first. Then, two indicators are proposed for detecting static eccentricity (SE) and dynamic eccentricity (DE), respectively. The amplitudes of the SE and DE indicators are proportional to the fault degree. The angle of the SE indicator proves to be the direction of SE. Meanwhile, two indicators show excellent robustness and are independent of loads and rotation speed. Moreover, these indicators can be applied in any surface-mounted PMSG with a three-multiple number of slots. Accordingly, an algorithm to diagnose the eccentricity fault is shown based on two indicators from three sensing points outside. The computation of the method is light, which leads to fast detection speed. Finally, the accurate results in multioperating conditions from simulations and experiments verify the feasibility of the proposed approach.