We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation Politano and Pouquet, Phys. Rev. E 57, 21 1998 between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is notsimply proportional to the relative separation. Possible implications for laboratory and space plasmas are discussed.