“How long does it take for a tooth extraction gap to close with Invisalign?”

The time for complete closure varies with each patient and which tooth was removed.  Molars being the largest, take more time while mandibular incisors may only take a month or two.  Don't take it too fast because damage can occur to the roots of the teeth if the movement occurs too quickly. Therefore, you shouldn't put new trays in until it is time, the results can be troublesome.
hope this helps, Dr. G.  

It depends on your age, the size of the gap, your bite and how much room there is.

That depends on the tooth being moved. Front teeth can move more quickly and there is less distance to move, so maybe within 2 months.  Back teeth are bigger and move through denser bone so it can take several months.