We present the results of optical and near-IR spectroscopy and multicolor photometry of the emission-line star MWC 645, which exhibits the B[e] phenomenon. The presence of positionally variable absorption lines of a cool star detected for the first time indicates that the object is a binary system. Using a combination of the photometric and spectroscopic data as well as the Gaia EDR3 distance (D=6.5{+/-}0.9kpc), we disentangled the components' contributions and estimated their surface temperatures and luminosities (18000{+/-}2000K and 4250{+/-}250K, log(L/L{sun})=4.0{+/-}0.5 and 3.1{+/-}0.3 for the hot and cool components, respectively). Quasi-cyclic short-period (months) and long-period (~4yr) photometric variations were detected in both optical and near-IR regions, and are most likely due to variable circumstellar extinction. Our analysis suggests that MWC 645 is a member of the FS CMa group. The object's properties can be described by an evolutionary model of a close binary system that currently undergoes a nonconservative mass transfer between intermediate-mass stars (e.g., 7M{sun}+2.8M{sun}).