She has not shown that she is not a ghost. For example, in one episode she said she had to go to the bathroom and in another episode, she tried to sit down and she fell taking physical damage from the fall.
Major spoilers ahead, be warned. Like suggested by Omry, maybe reading the manga or watching the anime if it closes up, maybe also Fairy Tail Zero, would be better than reading my answer. But anyway here it comes:
Mavis is, like Zeref, burdened with the Ankhseram Black Magic curse. This happend because she casted the magic "Law" in an incomplete state. The curse's direct effect - immortality - is the reason she didn't mature anymore, afterwards.
After the death of a guild member (Rita, Makarov's mother), which was most likely caused by the second effect of the curse (the more she cares about life, the more people would die), she fled and wandered around, trying to kill herself by starving.
After one year Zeref found her, of course still alive because of the curse. They came to love each other (another story), but their kiss caused Zerefs curse to kill Mavis, though she should be immortal.
But the curse still affected her, so she didn't die completly. Zeref brought her "corpse" to Precht, who sealed it inside the giant Lacryma after noticing there was still magic energy inside the body. And that's the reason she can still interact with the world in her ethereal body.
If the question was, whether her "body" is really a ghost, the answer should be yes. Ethereal bodies like her do not exist physically, so it's basically a ghost like we'd normally think of it. She created the body on Tenryou island after the S-Class exam using magic, so she has kinda shown that it's not real.
I don't think she really took phyiscal damage when falling, it's just that she was interacting with the physical world because she liked to. That's pure speculation, though.