The INTEGRAL satellite has revealed a previously hidden population of absorbed high-mass X-ray binaries (HMXBs) hosting supergiant (SG) stars. Among them, IGR J16320-4751 is a classical system intrinsically obscured by its environment, with a column density of ~10$^{23}$ cm$^{-2}$, composed by a neutron star (NS, spin period ~1300 s), accreting matter from the stellar wind of an O8I star, with an orbital period of ~9 d. We analyzed all archival XMM-Newton and Swift/BAT observations, performing a detailed temporal and spectral analysis of its X-ray emission. XMM-Newton light curves show high-variability and flaring activity on several timescales. In one observation we detected two short and bright flares where the flux increased by a factor of ~10 for ~300 s, with similar behavior in the soft and hard X-ray bands. By inspecting the 4500-day light curves of the Swift/BAT data, we derived a refined period of 8.99$pm$0.01 days. The XMM-Newton spectra are characterized by a highly absorbed continuum and a Fe absorption edge at ~7 keV. We fitted the continuum with a thermally Comptonized model, and the emission lines with 3 narrow Gaussian functions using two absorption components, to take into account both the interstellar medium and the intrinsic absorption. We derived the column density at different orbital phases, showing its clear modulation. We also show that the flux of the Fe K$alpha$ line is correlated with the NH column, suggesting a link between absorbing and fluorescent matter that, together with the orbital modulation, points towards the SG wind as the main contributor to both continuum absorption and Fe K$alpha$ emission. Assuming a simple model for the SG wind we were able to explain the orbital modulation of the absorption column density, Fe K$alpha$ emission, and the high-energy Swift/BAT flux, allowing us to constrain the geometrical parameters of the binary system.
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