In the original form of the game from which chess probably derived, chaturanga, there was no piece named "Queen".
The Queen of modern chess probably derived from a piece named "General": in the beginning this piece could move 1 square only diagonally, then its movenemt became more and more similar to the modern Queen. But there's more: in chaturanga there were pieces very similar to pawns, "Soldiers", that could become Generals after having reached opponent's King field.
When chess was imported in Europe, during Middle-Age and Reinassance, passing especially through Spain, pieces were renamed in order to give european players a more comfortable playing background. For example, the uncommon "Elephant" became "Bishop" (a very well known figure in catholic regions). And the General became the "Queen". But they only renamed pieces without changing the mechanic of the game. Thus, a "Soldier" could (and can) still be promoted.