The support of a localized three-dimensional neuronal current distribution, within a conducting medium, is not identifiable from knowledge of the exterior magnetic flux density, obtained via Magnetoencephalographic (MEG) measurements. However, this is not true if the neuronal current is supported on a set with dimensionality less than three. That is, the support of a dipolar current distribution can be recovered if it is a set of isolated points, a segment of a curve, or a surface patch. In this work we provide an analytic algorithm for this inverse MEG problem and apply it to the case where the current is supported on a localized disk having arbitrary position and size within the brain tissue. The proposed recovery algorithm reduces the identification of the characteristics of the current to the solution of a nonlinear algebraic system, which can be handled numerically.