We may not be used to hearing it, and we may not like the way it sounds, but grammatically there is nothing wrong with it. "Tomorrow" is a noun, the object of the prepositional phrase "on tomorrow." The entire prepositional phrase is adverbial, but the word "tomorrow" by itself is a noun. Whether we say or write "on" or not, structurally it is there.
On Tomorrow
We may not be used to hearing it, and we may not like the way it sounds, but grammatically there is nothing wrong with it. "Tomorrow" is a noun, the object of the prepositional phrase "on tomorrow." The entire prepositional phrase is adverbial, but the word "tomorrow" by itself is a noun. Whether we say or write "on" or not, structurally it is there.