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An efficient technique is presented to compute the scattering from one-dimensional (1-D) periodic microstrip structures, illuminated by a plane wave under perpendicular incidence. The technique relies on a Mixed Potential Integral Equation (MPIE), discretized by the Method of Moments (MoM), solving for the unknown current density flowing within a unit cell of the periodic structure. The pertinent 1-D periodic Green's functions are obtained by invoking the Perfectly Matched Layer (PML)-paradigm. The proposed formalism is illustrated and validated by evaluating the scattering from a 1-D periodic microstrip patch array.