Can Invisalign Fix the Gap Between Top and Bottom Teeth?

Open bites (when your top and bottom teeth do not touch) are very difficult to correct and maintain and thus, I would recommend getting an orthodontic consult in order to better understand your malocclusion and treatment options. There are dental open bites (which are a result of the teeth being in the wrong position) and there are skeletal open bites (in which the maxilla and/or mandible is in the wrong position). Whether or not your case can be treated with braces and elastics or braces and surgery will be determined with the diagnostic records.
Invisalign can be used to straighten your teeth and possibly improve the open bite slightly, but full correction will require braces (with possible surgery or mini-screws)
The most difficult issue with correcting open bites is the long term stability and this should be considered.

Do not invest in Invisalign if you want to close the gap between the upper and lower teeth. This gap is called an "Open Bite".
An "Open Bite" is when the front teeth don't touch when closing together on your back teeth. Invisalign will not successfully pull the front teeth together. They make this very clear on their website and any doctor attempting to do it, is destined for failure. To make matters worse, even with braces, open bites are very prone to relapse--reopening after treatment (even if retainers are worn well). Often surgical orthodontics is necessary for successful open bite closure.
With that said, Invisalign could align your upper and lower teeth but it will NOT close the gap between the two.