We characterise the relation between the gas and dust content of the interstellar medium towards young stellar objects in the Orion Nebula Cluster. X-ray observations provide estimates of the absorbing equivalent hydrogen column density NH based on spectral fits. Near-infrared extinction values are calculated from intrinsic and observed colour magnitudes (J-H) and (H-Ks) as given by the VISTA Orion A survey. A linear fit of the correlation between column density and extinction values AV yields an estimate of the N_H_/A_V_ ratio. We investigate systematic uncertainties of the results by describing and (if possible) quantifying the influence of circumstellar material as well as the adopted extinction law, X-ray models, and elemental abundances on the NH/AV ratio. Assuming a Galactic extinction law with R_V=3.1 and solar abundances by Anders et al. (1989), we deduce an N_H_/A_V_ ratio of (1.39+/-0.14)*10^21cm^-2^.mag^-1^ for Class III sources in the Orion Nebula Cluster, where the given error does not include systematic uncertainties. This ratio is consistent with similar studies in other star-forming regions and approximately 31% lower than the Galactic value. We find no obvious trends in the spatial distribution of N_H_/A_V_ ratios. Changes in the assumed extinction law and elemental abundances are demonstrated to have a relevant impact on deduced A_V_ and N_H_ values, respectively. Large systematic uncertainties associated with metal abundances in the Orion Nebula Cluster represent the primary limitation for the deduction of a definitive N_H_/A_V_ ratio and the physical interpretation of these results.