The prefecture was devastated by an earthquake and tsunami in March 2011 that triggered the worst nuclear accident since Chernobyl in 1986.
Baseball is returning to the Olympics for the first time since 2008 at the Tokyo Games and organisers are keen to play a part in helping the region - parts of which are still uninhabitable - get back on its feet.
Speaking on the sidelines of the International Olympic Committee's Executive Board meeting in Pyeongchang, host of next year's Winter Games, Mori said there was no better way to showcase Japan's recovery from the national tragedy.
"It's the Tokyo Games but one match, probably the opening match, will go to Fukushima Stadium," he said through a translator, adding that the Azuma venue would also host at least one softball match.
"Tokyo 2020 is a showcase for the recovery and reconstruction of Japan from the disaster of March 2011, so in many ways we would like to give encouragement to the people, especially in the affected area."
Mori said the "fantastic idea" to play a game in the affected area had originated in a meeting between IOC President Thomas Bach and Japanese Prime Minister Shinzo Abe last October.
He added that Fukushima prefecture had also offered to cover the costs of the refurbishment and renovation work needed for the stadium to get ready for the Games.
Riccardo Fraccari, president of the World Baseball Softball Confederation, welcomed the decision.
"WSBC congratulates Tokyo 2020 President Mori and IOC President Bach on this great step taken with Olympic baseball and softball as a vehicle to inspire hope and highlight the regeneration in Fukushima," he said in a statement.
"It is a tremendous honour and a duty we take very seriously to be a part of something so meaningful - to serve the Olympic movement and to use the power of sport to shape a better world."
(Editing by Nick Mulvenney)
