Yes. It will grow back but it will take a couple of months for it to happen. Until then, you may see a thin membrane form to cover where the toenail used to be. I would keep it covered and be sure to wear socks with your shoes so that no fungus/sweat gets in there. And wash it well each night with an antibacterial soap or peroxide.
But you should see a new toenail within a month or so.
Let me know if you still have questions.