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 N_H based on spectral fits. Near-infrared extinction values are calculated from intrinsic and observed colour magnitudes (J-H) and (H-K_s) as given by the VISTA Orion A survey. A linear fit of the correlation between column density and extinction values A_V 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 and the adopted extinction law, X-ray models, and elemental abundances on the N_H/A_V ratio. Assuming a Galactic extinction law with R_V=3.1 and solar abundances by Anders & Grevesse (1989), we deduce an N_H/A_V ratio of (1.39 +- 0.14) x 10^21 cm^-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.

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