We extend to the magnetohydrodynamic (MHD) case a recent model of intermittency due to She and L\'ev\^eque [Phys. Rev. Lett. 72, 336 (1994)]. The model that we develop in the framework of the Iroshnikov-Kraichnan theory of MHD turbulence depends on two parameters that are linked to anomalous scaling laws of dissipative structures when their characteristic scale l\ensuremath{\rightarrow}0. A brief comparison with published data stemming from spacecraft observations within the solar wind shows that it is a workable model and that within the framework of the model, dissipative structures in MHD turbulence are sheetlike, as observed in recent numerical simulations in three dimensions at moderate Reynolds numbers.