The answer is "it depends".
It depends on the Antenna design, but lets look at an example:
A typical (license free / home / consumer) installation of WiFi is 100mW (not a 1000mW as your post indicates)
A typical antenna has a 50 Ohm impedance, and lets take an example:
For a 1/4 wave vertical antenna the voltage distribution has a voltage minimum at feed point, and a voltage maximum at the end. And lets take that this antenna has a perfect Resistance part of the complex Impedance = 50 + 0j Ohm (in practice this may vary a lot)
Ohm's Law will show you E = SQRT(P*R) = SQRT(0.1*50) = 2.23 V (at the antenna tip)
This is only true for the standard quarter-wave vertical, other antenna designs may have different voltage distribution.
An antenna may have a rating of "20 W" but that only indicates the maximum power input possible with that antenna before "things go bad".
You will have to check local legislation on what the maximum power is you may run, but as indicated above in many regions of the world this is 100mW (YMMV)
Often this is expressed in ERP, so it will take antenna gain into account. Example: If your antenna has a unity gain of 3dB, then you need to ensure that the transmitter (the WiFi Router) is throttled back to 50mW in order to be compliant with a 100mW-ERP legislation. This assumes no cable loss, so the actual calculation will be more complex taking cable loss / connector loss into account.