Mauricio Pochettino's men trail the Foxes by seven points with two games left to play.
"We've had our peaks before. This one, though, is bigger than sport. It has much more human interest in it," Scudamore told The Times.
"It's a life-affirming story, which is why it's attracted more interest than you'd normally get.
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"It's from whence they've come... It's the most remarkable thing that's ever happened in my lifetime, and probably anybody's lifetime, in terms of a football, sporting story, and that's not over hyping it.
"We've never seen the likes of it before and we may never see the likes of it again."
Leicester host 11th-placed Everton in the league at the King Power Stadium on Saturday after which they will be presented with the Premier League trophy.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
