The smallest Rubik’s Cube is10 mm (0.39 in) wide and was created by Evgeniy Grigoriev (Russia). It is fully functional and can be used like a normal Rubik’s Cube.

It is 2mm smaller than the previous one he made.
http://thatstoday.com/article/2801165/evgeniy-grigoriev-creates-worlds-smallest-rubiks-cube