We consider the flow of quasi-Newtonian fluid through a thin porous media. The media under consideration is a bounded perforated three dimensional domain confined between two parallel plates, where the distance between the plates is described by a small parameter ε. The perforation consists in an array of solid cylinders, which connect the plates in perpendicular direction, with diameter of size ε and distributed periodically with period ε. The flow is described by the three dimensional incompressible stationary Stokes system with a non-linear viscosity following the Carreau law. We study the limit when the thickness tends to zero and prove that the averaged velocity satisfies a non-linear two dimensional homogenized law of Carreau type.