Super Smash Bros. for Wii U: Not Compatible with Nintendo Wii

No. Super Smash Bros. for Wii U (2014) is exclusive to the Wii U console. It cannot run on the original Wii.

Why

• Hardware: Wii U has a tri-core PowerPC CPU (1.24 GHz), 2 GB RAM, and a GPU supporting modern shaders. Wii has a single-core Broadway (729 MHz), 88 MB RAM, fixed-function GPU.
• GamePad Dependency: Menus, stage builder, Smash Tour, and some moves rely on the Wii U GamePad's touchscreen and second-screen output.
• Disc Format: Wii U uses proprietary 25 GB discs; Wii drives cannot read them.

Wii Smash Option

Super Smash Bros. Brawl (2008) is the Wii entry. It supports GameCube controllers, Wii Remotes, Classic Controllers, and has Subspace Emissary (story mode). Still playable today—active mod scene (Project M, Brawl Minus) via Homebrew.