Refrigerator water line leaking even though not hooked up
If you are talking about the water supply to the fridge from the house the valve may have been bumped. If you can find the valve try and turn it off "lefty loose right tight" (I still have to remind my kids that sometimes LOL). If you find a Saddle valve that looks like this these are notorious for leaking at the connection point and dripping when not connected. the valve may need to be replaced. Hope that helps.
At first I thought you were talking about the fridge itself but after re reading revised, putting both in just in case.
If the water is dripping out of the tube on the refrigerator where you normally supply water to it, it will stop soon. Once a little air got into the tube the system started to empty out. To speed things up pull the water filter if it has one and trip the water in the door these will remove some water and allow more of the water in the system to drain out quickly.  There is nothing wrong or to worry about.