The increasing demand for controlling electromagnetic waves has led to the construction of a variety of metasurface absorbers with different functionalities. In this Letter, we designed a kind of single-layer metasurfaces with delicately designed hybrid magnetic meta-atoms (HMMAs), which can be operated as perfect absorbers (PAs) for the electromagnetic wave incident at a specified direction, but at the mirror symmetric direction, the nearly total reflection is achieved. This remarkable nonreciprocal phenomenon arises from the time-reversal symmetry (TRS) breaking nature of magnetic surface plasmon as well as the lattice Kerker effect due to the interaction of HMMAs in the single-layer metasurfaces. In addition, the nonreciprocal effects are also associated with the nonreciprocal Fano resonances of HMMAs, and thus the performance of nonreciprocal PAs can be further modulated by engineering the HMMAs. The extraordinary functionalities of this nonreciprocal PA make it promising for the nonreciprocal optics and the microwave photonics.