This work concerns the Stokesian flow of an axisymmetric, incompressible couple stress fluid through a porous medium which encloses a solid sphere, under a uniform magnetic field. The problem is solved analytically by using separation of variables technique and expressions for stream function, velocity components, vorticity component, fluid pressure, stress tensors and couple stresses are obtained in terms of modified Bessel functions. A new result for drag force experienced by a solid sphere enclosed in porous medium under the applied uniform magnetic field is evaluated. Some special cases for flow past the impermeable sphere are obtained and validated by the existing results. Also, a well-known result of drag force for the Stokes flow past an impermeable sphere is reported. The profiles of tangential velocity, drag force and patterns of streamlines are plotted for different values of flow parameters.