How Long Will It Take Invisalign to Close Gap from Tooth Extraction?

The teeth which are removed are the first premolars. And the aligners can close the gap  between 3 to 6 months. The rapid movement  at orthodontic treatment can damage your tooth and cause root resorption. 

If the space is large it will take a long time since Invisalign moves teeth slowly. Invisalign is better at tipping the tooth rather than moving the whole tooth and root. If the space is big, I ask, why aren't you going with a dental implant to replace the space, or why aren't you enlarging the space to place an if it isn't big enough? If you are already into treatment, this may not be an option anymore, but if you haven't begun, you may be able to plan for an implant. I would look into it.

However, Invisalign can put a fake tooth in the aligner so it looks like you have a tooth there while the gap closes. It can take longer to move a tooth through the bone than keeping it in place and rotating or tipping it, but, depending on how large of a gap you have, it can be accomplished in time.

A nice thing about Invisalign is that it works in a slow and controlled fashion. Teeth that move too quickly can be damaged and lost due to resorption. Invisalign by default moves teeth at about 0.2 mm per aligner, so a bit less than 1/2 mm per month. If you have 14 mm to close, plan on 28-30 months, or 2.5 years. Sometimes the space is not large due to the tooth that was extracted had been pushed out of the way (or crooked), leaving a gap of 8-10 mm, taking 16-20 months.