The powerful Pokemon first appeared in Pokemon Red & Blue, and was difficult to capture without a Master Ball.
To acquire the rare Pokemon, players must be online and have no more than 11 wonder cards in their possession, according to IGN.
They must select the Mystery Gift option from the main menu and receive the gift to see Mewtwo in their game.
Mewtwo will start at level 70 with the moves Shadow Ball and Electro Ball. A new signature move named Psystrike will also be learnt, which inflicts damage based on enemy defense.
It also comes holding a King's Rock, which can make opponents flinch and miss their attacks, as well as a Premier Ribbon.
The promotion will run from February 12 to February 26.
Pokemon Black & White was released on Nintendo DS last year and sold over one million units at launch.
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Watch a trailer for Pokemon Black & White below: