I have the same problem with my small Zelda figures (mfc link)
The yellow part of link and tetra are extreme sticky. Tried to wash it away but failed.
I think it's the softener that comes out :/
They stay on my manga shelf so they are permanent on the air
[ext link ] *shameless self-promotion*
I noticed this happen to some nib figures I owned. I deboxed them and they were pretty sticky. Unfortunately this happens when you keep figures new in their box or even in a glass cabinet. Like everyone has said, just put her in a warm mixture of water and dish soap. It can take a few times but it will remove the stickiness and leave your figure clean. Also, be sure to keep the case door open (if you have her enclosed) and let her air out once in a while and make sure to clean dust too!
Take it apart as best you can and throw it in a bowl of warm water with a bit of dish soap overnight. It might not work the first time, I had to soak item #30798 for like 3 days, changing the water 3 times, but the stickiness was pretty much gone.
As Ose_93 said you can wash it to remove the stickiness. I usually just use mild hand soap and gently rub the figure and rinse until clean. The stickiness is from the plasticizer (which makes the figure feel soft) evaporating and having no where to go. It will evaporate over time and if it's in open air it won't get sticky.
The only way I've heard of to prevent it is to routinely stick the figure in the freezer for a while to stop it evaporating, but I've never bothered. As long as you let it air out regularly it will be just fine. The plasticizer evaporating won't damage the figure, it just won't feel as soft.
bit old, but still usefull
[ext link ]
This is an older figure, the stickiness happens sometimes because the figures stay in their packaging and are not "aired out".
You can wash her with alcohol-free dish soap to try to get rid of the stickiness.