In Illustrator CC you can go to File >> Save As, then name your file and hit the Save button. That should bring up a dialog box that presents some additional save options, one of which will be "Save each artboard to a separate file."
I'm sure you can do this in previous versions of Illustrator as well, but since I have Illustrator CC installed, I can't confirm the exact workflow, but I assume the process is very similar.
Sorry, also...implied in my initial response is that first you would have to move each icon to it's own separate artboard prior to doing the steps I outlined above. That can be done by simply adding some additional artboards and moving one icon per artboard, so that each icon was on a separate artboard.