The optical reflection and transmission coefficients of a metallic nanograting have been studied with the use of numerical simulation in a wide range of the size of structural units of the grating. The grating is composed of silver nanowires arranged periodically on a quartz substrate. The cases of s- and p-polarized incident waves have been considered. In particular, it has been found that the spectral dependence of the reflection and transmission coefficients of the nanograting becomes oscillatory and exhibits several deep minima when all structural parameters of the grating (the nanowire’s width and height, and the grating period) approach tens of nanometers. The physical reason of the appearance of these oscillations has been analyzed. It has been shown how the depth and position of the discovered minima depend on the light angle of the incident wave and the rotation angle of the grating around its normal surface.