I've transplanted a lot of fig tree suckers, and I do similarly to what Bob C suggested, except that I cover them in plastic. I leave the leaves on (and as Pete pointed out, keeping the humidity high with the plastic serves essentially the same purpose that cutting off the leaves would do... whichever of those techniques you choose, the point is to prevent it from drying out). I leave the leaves on, cover it in plastic to keep humidity high, and in order to avoid mold I air it out well each day. Usually they lose some of the leaves anyway. One other tip: avoid the temptation to overwater it. Stay patient and keep the humidity up, and keep it in the shade (I usually keep in shade for a couple of weeks, then gradually move to brighter spots (part of the day at first). Good luck... odds are very good for it to survive I think, though depending on how quickly the roots acclimate it seems likely you'll lose the figs on it. Good luck!
Mike