Not directly but worth checking out The Room, some of the Gobliiins games (phone only I think), both of the Monkey Island special edition re-releases (1 & 2) and Tiny Bang Story which looks visually most similar but it's much more kid-friendly casual gameplay I warn you:
If you have a Mac or PC you could try the same devs newest game Botanicula: http://amanita-design.net/games/botanicula.html
...it's on Steam I think.
And shameless plug but you could try City of Secrets by a company I work with
Really enjoying machinarium now... Are there any similar games?
similar in what sense? The aesthetics? The gameplay? The touchscreen is a pretty awesome way to play these adventure/point & click games and developers probably know that! There are many ports/rebuilds of PC & console point & click games in the App Store