Actually, our only specific reference to wheat in Tolkien's tales is to the golden wheat of the Valar that grew tall in the fields of the Blessed Realm beyond the Great Sea. Nonetheless, we can assume that wheat was also grown in Middle-earth, if only because it continues to exist in the world today.

Though this is the only explicit use of the word 'wheat', there are various references to 'corn' growing widely in Middle-earth. The word 'corn' can have various meanings, in this particular context it can probably be taken as a reference to wheat.

Modern English 'wheat' derived from Old English hwæte, and connected words are found in numerous other languages. All these variants ultimately derive from an ancient word for 'white'.