We investigate the afterglow of GRB 140713A, a gamma-ray burst (GRB) that was detected and relatively well-sampled at X-ray and radio wavelengths, but was not present at optical and near-infrared wavelengths, despite searches to deep limits. We present the emission spectrum of the likely host galaxy at $z = 0.935$ ruling out a high-redshift explanation for the absence of the optical flux detection. Modelling the GRB multi-wavelength afterglow using the radiative transfer hydrodynamics code BOXFIT provides constraints on physical parameters of the GRB jet and its environment, for instance a relatively wide jet opening angle and an electron energy distribution slope $p$ below 2. Most importantly, the model predicts an optical flux about two orders of magnitude above the observed limits. We calculated that the required host extinction to explain the observed limits in the $r$, $i$ and $z$ bands was $A^{rm host}_{V} > 3.2$ mag, equivalent to $E(B-V)^{rm host} > 1.0$ mag. From the X-ray absorption we derive that the GRB host extinction is $A^{rm host}_{rm V} = 11.6^{+7.5}_{-5.3}$ mag, equivalent to $E(B-V)^{rm host} = 3.7^{+2.4}_{-1.7}$ mag, which is consistent with the extinction required from our BOXFIT derived fluxes. We conclude that the origin of the optical darkness is a high level of extinction in the line of sight to the GRB, most likely within the GRB host galaxy.
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