Context. IGR J06074+2205 is a poorly studied X-ray source with a Be star companion. It has been proposed to belong to the group of Be/X-ray binaries (BeXBs). In BeXBs, accretion onto the neutron star occurs via the transfer of material from the Be star’s circumstellar disk. Thus, in the absence of the disk, no X-ray should be detected. Aims. The main goal of this work is to study the quiescent X-ray emission of IGR J06074+2205 during a disk-loss episode. Methods. We obtained light curves at different energy bands and a spectrum covering the energy range 0.4–12 keV. We used Fourier analysis to study the aperiodic variability and epoch folding methods to study the periodic variability. Model fitting to the energy spectrum allowed us to identify the possible physical processes that generated the X-rays. Results. We show that at the time of the XMM-Newton observation, the decretion disk around the Be star had vanished. Still, accretion appears as the source of energy that powers the high-energy radiation in IGR J06074+2205. We report the discovery of X-ray pulsations with a pulse period of 373.2 s and a pulse fraction of ~50%. The 0.4–12 keV spectrum is well described by an absorbed power law and blackbody components with the best fitting parameters: N_H = (6.2 ± 0.5) × 10²¹ cm⁻², kT_bb = 1.16 ± 0.03 keV, and Γ = 1.5 ± 0.1. The absorbed X-ray luminosity is L_X = 1.4 × 10³⁴ erg s⁻¹ assuming a distance of 4.5 kpc. Conclusions. The detection of X-ray pulsations confirms the nature of IGR J06074+2205 as a BeXB. We discuss various scenarios to explain the quiescent X-ray emission of this pulsar. We rule out cooling of the neutron star surface and magnetospheric emission and conclude that accretion is the most likely scenario. The origin of the accreted material remains an open question.