Nintendo of Japan revealed the news on its official Wii website (courtesy Kotaku translation), stating that Wii "manufacturing is scheduled to end soon." It offers no firm date after which the company will cease building Wiis, nor any official word on whether this move is exclusive to Japan or if it applies globally. We've reached out to Nintendo for clarification.
As Engadget points out, this decision should come as little surprise. Nintendo released the Wii's successor nearly a year ago, and has long since turned its PR efforts toward the new machine. Further, the Wii U has been able to play Wii games since day one. Its most recent update even allows players to enjoy Wii software on the new system's portable GamePad screen.