Aims. Following the recent detection of 36ArH+ in the Crab nebula spectrum, we have computed the photodissociation rate of ArH+ in order to constrain the physical processes at work in this environment. Methods. Photodissociation cross sections of ArH+ are computed in an ab initio approach including explicit account of spin-orbit coupling. Results. We report the photodissociation cross section of ArH+ as a function of wavelength. Photodissociation probabilities are derived for different impinging radiation fields.The photodissociation probability of for a very small unshielded cloud surrounded on all sides by the unshielded InterStellar Radiation Field (ISRF) model described by Draine (1978) is equal to 9.9e-12 s-1 and 1.9e-9 s-1 in the Crab nebula conditions. The dependence on the visual extinction is obtained by using the Meudon Photon Dominated Region (PDR) code and corresponding analytical fits are provided. Conclusions. These data will help to produce a realistic chemical network to interpret the observations. Photodissociation of ArH+ is found to be moderate and the presence of this molecular ion is mainly dependent on the molecular fraction

11 pages, 6 Figures, Accepted in Astronomy Astrophysics