The title reaction is investigated using a semiclassical coupled wave packet method where the hyperspherical radius rho is treated classically and the other coordinates quantally. Dynamical calculations are performed in a coplanarlike approximation using eight coupled electronic states. State-to-state reaction cross sections are obtained in the energy range 0.3 eV less than or equal to E(coll)less than or equal to 5 eV for five different initial rovibrational states. The internal energy of the ArH+ product is found to be very high, especially at low collision energy. A comprehensive analysis of the reaction mechanisms is presented.