Context. Very few examples of luminous blue variable (LBV) stars or LBV candidates (LBVc) are known, particularly at metallicities below that of the Small Magellanic Cloud (SMC). The LBV phase is known to be crucial for the evolution of massive stars, and its behavior with metallicity is very poorly known. Variable star V39 in IC 1613 is a well-known photometric variable, with changes in the B-band by more than one magnitude over a period of 14 or 28 days, and with amplitudes decreasing with wavelength. The star, which has also been proposed to be a peculiar system consisting of a Galactic W Virginis and an IC 1613 red supergiant, displays characteristics that render it a possible LBVc. Aims: We explore the nature of V39 and obtain an estimate of its physical parameters. Methods: We investigate the behaviour of intermediate resolution blue and red spectra obtained with VIMOS at the Very Large Telescope (VLT) covering a time span of 40 days in the frame of our spectroscopic studies of massive stars in IC 1613, and perform a quantitative analysis of the combined spectrum by means of the model atmosphere code CMFGEN. Results: We identify strong P-Cygni profiles in Balmer and Fe ii lines of V39, and also a hybrid absorption spectrum that resembles an early type supergiant (B-A) in the blue and a late type star (G) in the red. No significant radial velocity variations are detected, and the spectral changes are moderate although our individual spectra cover more than a photometric period. The model atmosphere analysis under the assumption of an individual star places V39 in the low-luminosity part of the LBV and LBVc region, although it would be also consistent with a sgB[e] star. From this analysis and the data in the literature we find evidence that the [α/Fe] ratio in IC 1613 is slightly lower than solar. Conclusions: The radial velocities of individual spectra indicate that V39 belongs to IC 1613. The lack of significant radial velocity changes and spectroscopic variations excludes binary scenarios, particularly those with close companions. The features observed are not consistent with a W Virginis star, and this possibility is also discarded. We propose a scenario in which the star is a B-A LBVc or sgB[e] star surrounded by a thick disk precessing around it and producing the composite spectral appearance. If confirmed, V39 would be the lowest metallicity resolved LBV candidate known to date. Alternatively, it could represent a new transient phase of massive star evolution, an LBV impostor. Based on observations obtained at the ESO VLT for Programmes 078.D-0767 and 080.D-0423.