Only iodine (I2) stains, iodide (I−) does not.
I2 dissolves in water very poorly, so rinsing with water will not help (much).
I− on the other hand, dissolves in water very readily and what’s more: it’s colourless.
So what you do is turn the I2 in you stain to I− and then rinse it off/out. You do this by putting vitamin C powder – dissolved in a little water – on the stain. The vitamin C turns the iodine into iodide and voila, your stain is gone. You have to get rid of the iodide though (rinse it out with water) because it might oxidize and turn back into iodine.
If the iodine is already well and truly sucked into you wash basin or floor or some cloths or whatever, you can also just wait. Iodine will evaporate at some point. It does this in its own pace of course. Depending on how deeply it has been absorbed and in what, it might take up to a week, but it will go away.