I'm afraid to say it, but sounds like you're going to need to replace the wood.
If it's just the area on the bottom, it should be fairly easy to do...but make sure to check the floor underneath it for water damage also.
After having to consult mold experts (we had toxic mold in the walls of the last house we rented, caused by a leak in the plumbing that had been fixed ages before), we found that the high humidity in the W. Washington area can actually keep established mold alive and growing even if a leak has been fixed. If you just cover an area up, you'll be risking having the mold spread into the rest of your wood & drywall in the house.
- If you can smell it...you're inhaling spores. (The toxic kind is RARE, but inhaling other kinds of mold aren't great for us either.)
- Wood rot sucks. It's better to replace a small thing now (and check to make sure no structural elements got hit), than to deal with a larger problem later.
www.thisoldhouse.com has many useful articles, both about replacing damaged elements, and about mold (much of the reconstruction of Katrina has to deal with this pervasive issue).