A tee is not required.
2-24-5,6 and 7 are relevant definitions.
A free kick (2-25-5) requires a place kick (2-24-7) or drop kick (2-24-6).
For a place kick (2-24-7) the ball must be in a fixed position on the ground *or* on a tee. The ball may also be held in place by a teammate, but it is not required to be held if it is not on a tee. The ball can be laying on the ground, but not moving (fixed position), and not held by a teammate either. I've had this happen a few times in JV games when the visiting team forgot to bring their tee and only discovered it on the opening kick off.