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\n Context. MWC 314 is one of the most luminous stars in the Milky Way. Its fundamental parameters are similar to those of luminous blue variables (LBVs), although no large photometric variations have been recorded. Moreover, it shows no evidence of either a dust shell or a relevant spectral variability. \n Aims. The main purpose of this work is to clarify the origin of the radial velocity and line profile variations exhibited by absorption and emission lines.\n Methods. We analyzed the radial velocity (RV) variations displayed by the absorption lines from the star’s atmosphere using high-resolution optical spectra and fitting the RV curve with an eccentric orbit model. We also studied the RV and profile variations of some permitted and forbidden emission lines of metallic ions with a simple geometric model. The behavior of the Balmer and He <sc>i</sc> lines has also been investigated. \n Results. Fourier analysis applied to the RV of the absorption lines clearly shows a 60-day periodicity. A dense coverage of the RV curve allowed us to derive accurate orbital parameters. The RV of the Fe <sc>ii</sc> emission lines varies in the same way, but with a smaller amplitude. Additionally, the intensity ratio of the blue/red peaks of these emission lines correlates with the RV variations. The first three members of the Balmer series as well as [N <sc>ii</sc>] lines display a nearly constant RV and no profile variations in phase with the orbital motion instead. The He <sc>i</sc> λ5876 Å line shows a strongly variable profile with broad and blue-shifted absorption components that reach velocities of ≤−1000 km s-1 in some specific orbital phases. \n Conclusions. Our data and analysis provide strong evidence that the object is a binary system composed of a supergiant B[e] star and an undetected companion. The emission lines with a non-variable RV could originate in a circumbinary region. For the Fe <sc>ii</sc> emission lines, we propose a simple geometrical two-component model where a compact source of Fe <sc>ii</sc> emission, moving around the center of mass, is affected by a static extra absorption that originates from a larger area. Finally, the blue-shifted absorption in the He <sc>i</sc> λ5876 Å line could be the result of density enhancements in the primary star wind that is flowing towards the companion, and which is best observed when projected over the disk of the primary star.\n