Look at it backwards.
- Why are you at zero G? Because your downward acceleration is equal to
the acceleration due to gravity.
- Why are you accelerating downwards so fast? Because you're not creating any lift to counteract gravity.
- Why are you not creating any lift? Because you are at zero degrees angle of attack!
And that's why you can't stall at zero G. You're always also at zero degrees angle of attack (you can get pedantic, depending how you measure it) when you're at zero G. And stalling is always caused by high angles of attack. And if that doesn't make 100% sense, you should look more into stalls before you dig too deep into how G loading affects stall speed.
EDIT: Many people here seem to be replacing the world "airplane" in the question with the word "wing". 0g flight involves the entire airplane, not just the wing. Sure, you could take a Cessna, strap highly controllable rocket engines to the top of it and drop it from another airplane. Then, use the rocket engines to counteract drag and give downward acceleration equal to the force of gravity. That would give you a stalled wing and 0g.
But that's not really an airplane anymore, and it doesn't really answer the question.
To stall, the wing must exceed the critical angle of attack. That means it must have an angle of attack above zero. That means lift is being created, which means an upward force is acting upon the airplane. That means you are no longer at 0g.
The point isn't that once an airplane is at 0g it becomes unstallable. The point is you have to leave 0g to stall it.
It's also an example of how airspeed is irrelevant to stalling. (Sounds crazy, since we talk about stalling speed!) Stalling isn't about the speed or amount of air flowing over the wings, it's about the angle, path and flow. A wing on the same airplane can be not stalled at 5mph, or stalled at 100mph. It just depends on the angle.