Sadly according to Jonathan Blow the game’s creator it has no chance of being made available on WiiWare, even though it is likely to appear on the Playstation Network in the future. Here’s what he had to tell EuroGamer:

WiiWare is not going to happen for this game because the model is just not right - like, Braid is too big of a game to be downloadable on WiiWare and stored on someone's Wii.

A lot of people think, oh, 3D is really complicated and is big, but 2D art - like all the bitmaps in Braid - takes a lot of space. The game is 144MB right now.

Again it seems that the lack of a storage solution is denying Wii owners the chance of playing a quality game. For now the solution is simple, buy a 360 too. Wii60 FTW!

Source: EuroGamer