There are 3 possible physical limits, depending on how pedantic the game is.
1*1 as that corresponds to the lowest mipmap a shader can use.
8*8 as that is the smallest JPEG compressed block one can do (there is no space saved going smaller).
32*32 as that is the smallest JPEG compressed block with downsized colour space that one can use (there is no space saved going smaller).
I do know that WC3 does have some multiple of 2 limit enforced on textures, however I am not sure if it can go down to 1 or will be stuck at 32 ish for other reasons.