The WPP-owned agency won the account from the incumbent, Starcom.
Mediaedge:cia's appointment is part of a wider global review by Nintendo, which also includes a review of the creative account.
The Japanese video games giant currently uses Publicis Groupe agencies to handle its creative account, with Leo Burnett handling the business in the UK market.
Nintendo has drawn up a longlist of creative agencies to pitch for the creative business. These agencies will start pitching for the business in two weeks.
Mediaedge:cia declined to comment on the story, while Nintendo claimed the review was still ongoing.
The global review was called because Nintendo wants to create a central marketing strategy, which is being pushed through by the company's head office in Japan.
Nintendo is attempting to broaden its appeal beyond the youth market.
To achieve this, the company is set to launch Touch Generations, a range of educational software aimed at an older demographic.