Both phrasings are correct and idiomatic. There is a subtle difference in emphasis, though. Including on the places emphasis and attention on the location, as opposed to the action of hitting. This makes the action seem more ordinary or routine, because the listener treats it as a matter of course. Conversely, without the preposition, the location is supplemental, and the most important information comes from hit.
This shifting of emphasis away from the verb can be used to signify intent, as T Romano noted in the comments, though of course that's not the only possibility; it can also be used to make a statement more formal or informational by adding linguistic distance, for example. Or perhaps the location was particularly unusual, and we'd like to draw extra attention to it.
A related aside: there's a parallel difference of emphasis when choosing between on and in for use with hit or strike. Again, on is more informational, while in either literally indicates something entering the body (such as a bullet: he was shot in the chest), or by suggesting force strong enough to move through the person. He was struck on the chest suggests a hit that bounced off, while in the chest conveys something stronger; maybe he doubled over, staggered, or fell backward.