Cosmological observations indicate that dark and luminous matter contribute similar energy densities to the present Universe: $\Omega_{DM} / \Omega_B \approx 5 $. This relation is naturally explained in Asymmetric Dark Matter (ADM) models by a common origin of the two, in which the DM relic density arises from particle-antiparticle asymmetry. Motivated by the leptogenesis mechanism to explain the Baryon Asymmetry of the Universe (BAU), we study the ADM scenario in the MSSM framework, with Higgsino-like neutralino as the lightest supersymmetric particle. We find the asymmetry generated at the Higgsino sector, and calculate the rate of the washout processes of this asymmetry. As a result, we obtain the MSSM spectrum allowing the Higgsino relic abundance to satisfy DM cosmological observations.