I think prayer plant does that, but it's a houseplant.

Sensitive plant....a variety of mimosa...rather common.
Linda C

Prayer plants don't respond to touch. Their form of response to environmental stimuli (tropism) is called nyctinastic tropism....reponse to night and day. Thigmotropism is the reponse to a physical touch of some sort. The Mimosa pudica ('Sensitive Plant) is a very common weed in many parts of the country, and considered an oddity by those who are not familiar with it. I've seen it sold in supermarkets, etc.

If this isn't the plant in question (it's impossible to tell from your description), I'd be surprised.

Here is a link that might be useful: {{gwi:1061504}}

I think rhizo1 is right. It could be Mimosa pudica. I remember it from a high school project about such peculiar plants. We used to call it "Touch-me-not". It would shrink back upon touching it.
Vaishali

I have a Mimosa pudica that I brought home for my daughter to tease. It is now over 4 feet in width and 1 foot high. I plan to use them as ground cover next year in one of my beds. It blooms regularly with fifty to one hundred of these little purple pom poms every few days or so. And actually, entire branches will droop in response to stimuli. It's a defense mechanism which exposes the thorns on the branches to animals attempting to eat the leaves.

{{gwi:829549}}
Mimosa pudica

If the stupid thing is a weed, then why is mine dying? :^(