It's not the best possible French, it is barely acceptable ; I personnally, wouldn't say it. That is language prompted by the need to express much in a few words and which therefore stretches the meaning of words to the point sometimes of making them special to only one situation; there is another usage of that sort in French, "commander dans un catalogue"; again, it's not the best possible way to say what corresponds to the action implied; it's better to say "commander à partir d'un catalogue".
There are numerous alternative ways to mention a menu and an order passed on the basis of a choice made from that menu.
Maurice commande son repas à partir d'une sélection qu'il fait sur la carte.
Maurice fait son choix sur la carte et passe sa commande.
Maurice lit la carte du menu puis passe sa commande.
Maurice choisit sa commande sur la carte et la passe au serveur au fur et à mesure.
There are other possibilities, such as "Après avoir parcouru la carte, Maurice passe sa commande."; note that in cases "2" and "4" the préposition is "sur"; this is correct because the menu is a sheet-like object; if it were a book-like object, such as a catalogue, you'd have to say "dans" (Elle a choisi cette robe dans un catalogue.).
It's worth noticing that the following combinations are not found in print (according to ngrams);
commande sur le menu, commander sur le menu, commandé sur le menu, commander sur la carte, commande sur la carte, commandé sur la carte