We present an analysis of the time-averaged spectrum of the Seyfert-2 active galaxy NGC 4388, obtained by NICER. The intrinsic strength of the reflection spectrum in NGC 4388, the large collecting area and favorable pass band of NICER, and a net exposure of 105.6 ks yielded an exceptionally sensitive spectrum. Using two independent families of models, the intrinsic spectrum from the central engine is found to be highly obscured but not Compton-thick. Enforcing physical self-consistency within each model, the independent treatments give formally consistent results: N_H = 2.67 (-0.03,+0.02) E+23 cm^-2 or N_H = 2.64 (-0.03, +0.03) E+23 cm^-2. Past measurements made with Suzaku and XMM-Newton are in broad agreement with these column density values. A more recent measurement with NuSTAR (in late 2013) recorded a column density about twice as large; the robustness of this variability is reinforced by the use of consistent models and procedures. The neutral Fe K-alpha line in the NICER spectrum is nominally resolved and consistent with an origin in the optical broad line region (BLR). The data also require ionized absorption in the Fe K band, similar to the warm absorbers detected in Seyfert-1 active galactic nuclei (AGN). The low-energy spectrum is consistent with a set of ionized plasma components. We discuss these findings and note that the geometric inferences that derive from this analysis can be tested with XRISM and Athena.