Understanding the method of inducing magnetism and the source of magnetism in two-dimensional (2D) materials is essential for the development of spintronic devices. Here, we present a spin-polarized first-principles study on the electronic and magnetic properties of a ZnO monolayer with adsorbed noble metals NM (NM = Pd, Pt, Ag, Au, Cu). The results demonstrate that the most preferable adsorption sites for all the considered noble metals NM (NM = Pd, Pt, Ag, Au, Cu) are located on top of the O atoms (T-O). Furthermore, both Pd and Pt adsorbed on the ZnO monolayer remain nonmagnetic. Interestingly, sufficient Ag, Au, and Cu adsorbates can induce magnetic properties, and the magnetic moments mainly originate from the adsorbates. Moreover, as the distance between the two atoms of the same element (Ag, Au, or Cu) increases, the ZnO monolayer undergoes FM-AFM transitions, which expand the utilization of ZnO monolayers in nanoelectronics and spintronics. These results may pave the way for future experiments based on 2D noble metal-adsorbed ZnO materials, which can serve as potential materials in nanoelectronics and spintronics.