Can I refrigerate pre-wrapped fresh fish in the wrapping from the store?

Yes. In fact, it is recommended. Food scientist Susan Brewer, Ph.D., explains why: "Every time you handle fish, it becomes contaminated by air, hands, and contact surfaces. Unless you plan to separate pieces of fish prior to freezing them, leave the fish in its original packaging.” You can refrigerate it in the paper supplied by the supermarket if it is tightly wrapped and taped up. If the fish is loosely wrapped, it should be re-wrapped. Because paper is somewhat permeable, it’s best to re-wrap the fish in plastic. Aluminum foil may leave a metallic taste. Put the wrapped fish in a shallow pan--not on a plate--and place it on the bottom shelf of your refrigerator to ensure drippings don't contaminate other products.
 

Source(s):
Brewer, M.S. and Chapman-Novakofski, K. 2006.  Meat Safety for the Consumer, University of Illinois Extension.
Susan Brewer, Ph.D.  University of Illinois, Department of Food Science and Human Nutrition