Well, it sounds kinda weird if you think about it. But it comes from "ssać" (to suck), because mammals suck their mom's milk... (can you say that in English? - well, anyway, you know what I mean).
Ok, it's a pretty similar etymology. I suppose what I was really wondering is how it ended up with a double letter at the beginning...
Hmm. I have no answer for that, but at least it's consistent with the verb ;)