Interesting question.
I'd say that, just as there is no minimum number of Pokemon in a deck, there is no minimum age to play.
However, one then gets into the rule of being able to actually conduct a game.
A deck with no Pokemon (Fossils excluded here) will not be able to engage in a real game.
If a player is so young that they cannot play the game, they would, unfortunately, lose due to that inability.
Imagine if there were some prodigy child of 3 years old that could read and follow the rules. That child could play. On the other hand, many six year olds would have problems playing effectively in a tournament without being disruptive.
We'll ask, though.