This work adapts the thin-wire approximation to the integro-differential formulation that models electromagnetic wave propagation through thin microstrip metasurfaces. A computationally efficient approach is achieved by reducing a surface current distribution to a filamentary electric current immersed in an effective dielectric medium. Besides, this is a general formulation that can be applied to wire and microstrip structures, even with lumped elements. Finally, this formulation is used to calculate the magnetic field through a magnetic metasurface lens excited by a wire loop. The results obtained agree on the overall behavior with full-wave simulation in commercial software, with almost 33 times faster computational time.