In the present study, silver (Ag) nanoparticles and maleic anhydride-grafted polyolefin elastomer (MAH-g-POE) were used as enhancement additives to improve the performance of the polyoxymethylene (POM) homopolymer. Specifically, the POM/Ag/MAH-g-POE ternary nanocomposites with varying Ag nanoparticles and MAH-g-POE contents were prepared by a melt mixing method. The effects of the additives on the microstructure, thermal stability, crystallization behavior, mechanical properties, and dynamic mechanical thermal properties of the ternary nanocomposites were studied. It was found that the MAH-g-POE played a role in the bridging of the Ag nanoparticles and POM matrix and improved the interfacial adhesion between the Ag nanoparticles and POM matrix, owing to the good compatibility between Ag/MAH-g-POE and the POM matrix. Moreover, it was found that the combined addition of Ag nanoparticles and MAH-g-POE significantly enhanced the thermal stability, crystallization properties, and mechanical properties of the POM/Ag/MAH-g-POE ternary nanocomposites. When the Ag/MAH-g-POE content was 1 wt.%, the tensile strength reached the maximum value of 54.78 MPa. In addition, when the Ag/MAH-g-POE content increased to 15wt.%, the elongation at break reached the maximum value of 64.02%. However, when the Ag/MAH-g-POE content further increased to 20 wt.%, the elongation at break decreased again, which could be attributed to the aggregation of excessive Ag nanoparticles forming local defects in the POM/Ag/MAH-g-POE ternary nanocomposites. Furthermore, when the Ag/MAH-g-POE content was 20 wt.%, the maximum decomposition temperature of POM/Ag/MAH-g-POE ternary nanocomposites was 398.22 °C, which was 71.39 °C higher than that of pure POM. However, compared with POM, the storage modulus of POM/Ag/MAH-g-POE ternary nanocomposites decreased with the Ag/MAH-g-POE content, because the MAH-g-POE elastomer could reduce the rigidity of POM.