Magnetic Skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as Skyrmion Hall effect. Extensive Hall data have further revealed asymmetry between Skyrmion and Anti-Skyrmion Hall angles, which cannot be accounted by known mechanisms. Here, we explain this asymmetry by utilizing another universal transport coefficient called `Hall viscosity,' extensively studied in quantum Hall systems. Hall viscosity is modeled in steady-state Skyrmions motion by generalizing the Thiele equation with a transverse velocity component and is independent of the Skyrmion charge. Our analyses, based on available asymmetric Hall angle data, reveal this transverse force amounts 3% - 5.4% of the force due to Skyrmion Hall effect. Further clarification of Hall viscosity will be essential for designing next generation storage devices properly, not to mention for our deeper understanding of fundamental properties of nature.