No. Wii U game discs are physically different (higher capacity, different format) and the Wii lacks the hardware (CPU/GPU/RAM) to run Wii U software.
However, the reverse works: The Wii U is fully backward compatible with nearly all Wii games. You can play Wii discs on the Wii U via "Wii Mode," which boots a virtual Wii environment. Wii U also supports Wii Remotes, Nunchuks, Classic Controllers, and Balance Board.